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John  3wett 


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2.  MA 
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7.  API 

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10.  INC 

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12.  GE< 

13.  ME 

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14.  AN 

15.  ZO< 

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16.  VE< 

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17.  SYS 

19.  ME 

20.  NA 

21.  NAUTICAL  ASTRONOMY.     By  Henry  Evers, 

22A  STEAM   AND  THE  STEAM  ENGINE— LAND  AND   MARINE. 

By  Henry  Evers,  LL.D.,  Plymouth. 
22B  STEAM    AND    STEAM    ENGINE— LOCOMOTIVE.     By    Henry 

Evers,  LL.D.,  Plymouth. 

23.  PHYSICAL  GEOGRAPHY.     By  John  Macturk,  F.R.G.S. 

24.  PRACTICAL  CHEMISTRY.     By  John  Howard,  London. 

25.  ASTRONOMY.     By  J.  J.  Plummer,  Observatory,  Durham. 


IN    COURSE    OF    PUBLICATION. 


ADVANCED    SCIENCE  SERI 

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Adapted  to  the  requirements  of  Students  in   Science  and  Art  Classes,  and 
Higher  and  Middle  Class  Schools. 

Printed   uniformly  in   izmo,  averaging  350  //.,  fiilly  Illustrated;  cloth 
extra,  price,  $1.50  each. 

1.  PRACTICAL  PLANE  AND  SOLID  GEOMETRY.    By  Professor 

F.  A.  Bradley,  London. 

2.  MACHINE     CONSTRUCTION     AND     DRAWING.     By     E. 

Tomkins,  Queen's  College,  Liverpool. 

3.  BUILDING  CONSTRUCTION.     By  R.  Scott  Burn,  C.E. 

4.  NAVAL   ARCHITECTURE— SHIPBUILDING  AND   LAYING   OFF. 

By  S.  J.  P.  Thearle,  F.R.S.N.A.,  London. 

5    PURE    MATHEMATICS.     By    Edward   Atkins,    B.Sc.,  (Lond.,) 
Leicester.     2  vols. 

6.  THEORETICAL  MECHANICS.     By  P.  Guthrie  Tail,  Professor 

of  Natural  Philosophy,  Edinburgh. 

7.  APPLIED     MECHANICS.     By    Professor   O.    Reynolds,   Owens 

College,  Manchester. 

8.  ACOUSTICS,  LIGHT  AND   HEAT.     By  W.  S.   Davis,  LL.D., 

Derby. 

9.  MAGNETISM    AND    ELECTRICITY.     By    F.    Guthrie,    B.A., 

Ph.D.,  Royal  School  of  Mines,  London. 

10.  INORGANIC  CHEMISTRY.     By  T.  E.Thorpe.  Ph.D.,  F.R.S.E., 

Professor     of    Chemistry,     Andersonian      University,     Glasgow. 
2  Vols. 

11.  ORGANIC  CHEMISTRY.     By  James   Dewar,    F.R.S.E.,  F.C.S., 

Lecturer  on  Chemistry,  Edinburgh. 

12.  GEOLOGY.     By  John  Young,  M.D.,  Professor  of  Natural  History, 

Glasgow  University. 

14.  ANIMAL  PHYSIOLOGY.     By  J.  Cleland,  M.D.,  F.R.S.,  Professor 

of  Anatomy  and  Physiology,  Galway. 

15.  ZOOLOGY.     By  E.  Ray  Lankester,  M.A.,  (Oxon.,)  London. 

16.  VEGETABLE   ANATOMY   AND    PHYSIOLOGY.     By   J.    H. 

Balfour,  M.D.,  Edinburgh  University. 

17.  SYSTEMATIC  AND  ECONOMIC  BOTANY.     By  J.  H.  Balfour, 

M.D.,  Edinburgh  University. 

19.  METALLURGY.     By  W.  H.  Greenwood,  A.R.S.M.     2  Vols. 

20.  NAVIGATION.     By  Henry  Evers,    LL.D.,  Professor   of  Applied 

Mechanics,  Plymouth. 

21.  NAUTICAL  ASTRONOMY.     By  Henry  Evers,  LL.D.,  Plymouth. 

22.  STEAM   AND  THE  STEAM  ENGINE— LAND,  MARINE,  AND 

LOCOMOTIVE.     By  Henry  Evers,  LL.D.,  Plymouth. 

23.  PHYSICAL  GEOGRAPHY.     By  John  Young,  M.D.,  Professor  of 

Natural  History,  Glasgow  University. 


ELEMENTS 


OF 


ACOUSTICS,  LIGHT,  AND  HEAT, 


BY 

WILLIAM    LEES,   M.A., 

LECTURER    ON    PHTSICS,   WATT     INSTITUTION    AND    SCHOOL    OF    AET8,    EDINBURGH] 
LATE    EXAMINER    IN    MATHEMATICS,   UNIVERSITY    OV    EDINBURGH. 


With 


NEW  YORK: 

G.   P.    PUTNAM'S    SONS, 

FOURTH  AVENUE    AND  TWENTY-THIRD   STREET. 
1873. 


i;PUCAT!ON 


PREFACE. 


THE  following  treatise  lias  been  prepared  in  strict  accord- 
ance with  the  syllabus  of  the  Government  Department  of 
Science  and  Art,  as  indicated  by  their  scheme  of  in- 
struction for  the  elementary  stage  examination,  in  the 
particular  branches  of  Acoustics,  Light,  and  Heat. 

Having  taught  these  subjects  for  several  years  to  large 
classes,  and  that  with  encouraging  success,  as  tested  by 
the  annual  examinations  of  my  students,  I  feel  the  less 
hesitation  in  complying  with  the  request  made  to  me  by 
the  Publishers,  of  giving  an  outline  of  the  course  which 
I  have  followed,  in  the  hope  that  it  may  be  found  useful 
to  others  engaging  in  the  discharge  of  similar  duties. 

While  instruction  in  the  branches  referred  to,  or  in- 
deed in  physical  science  generally,  is  essentially  depend- 
ent for  its  thorough  efficiency  on  extensive  and  minute 
experimental  illustration,  the  •  possession  on  the  part  of 
the  teacher  of  the  requisite  instruments  and  apparatus,  is 
of  course,  a  sine  qud  non. 

Special  references,  accordingly,  are  made  to  these,  and 
such  explanations  given  of  them  by  means  of  diagrams 

543  ?89 


4:  PREFACE. 

and  otherwise,  as  will  enable  the  student  to  understand 
their  construction  and  use,  and  thus  aid  him  towards 
acquainting  himself  with  the  leading  principles  of  these 
important  departments  of  science. 

At  the  end  of  each  subject  are  added  a  few  general 
questions,  similar  in  some  respects  to  those  that  have 
been  given  at  the  May  examinations. 

In  an  Appendix  I  have  made  a  selection  of  questions 
from  some  of  the  former  Government  papers,  and  have 
given  also  their  solutions.  These,  it  is  to  be  hoped,  will 
be  of  use  to  the  student  in  the  way  of  showing  him  how 
to  set  down  his  knowledge  of  the  subjects  for  the 
examiner. 

Though  many  excellent  books  on  Physics  have  been 
written  of  late  years,  both  in  our  own  country  and  on  the 
continent,  I  must  own  myself  more  especially  indebted 
to  the  works  of  Tyndall,  Ganot,  and  Deschanel.  For  a 
more  extensive  and  complete  knowledge  of  the  subjects 
in  question,  the  student  would  do  well  to  refer  to  these 
works. 

W.  L. 

LINKVALE  LODGE,  VIEWFORTH, 
EDINBURGH,  December,  1872. 


CONTENTS, 

ACOUSTICS. 
CHAPTER  I. 

PAGE 

Object  of  Acoustics — Cause  of  Sound — How  the  Air  is 
Affected — A  Sonorous  Wave — Wave-Length — Sound 
not  Transmitted  through  a  Vacuum  —  Velocity  of 
Sound — Elasticity  and  Density — Influence  of  Temper- 
ature— Changes  of  Temperature  in  a  Sonorous  Wave,  9 

CHAPTER  II. 

Intensity  of  Sound— Propagation  of  Sound  through  other 
Media— Table  of  Velocities  through  Different  Sub- 
stances— Reflection  of  Sound — Echoes — Refraction  of 
Sound — Structure  of  the  Ear,  ...  -  14 

CHAPTER  III. 

Physical  Difference  between  a  Musical  Sound  and  Noise — 
Pitch,  Intensity,  and  Quality  of  Musical  Sounds — 
Method  of  Determining  Number  of  Vibrations  — 
Sonometer — Influence  of  Sound-Boards — Resonance 
— Nodes  and  Ventral  Segments — Laws  of  the  Vibration 
of  Strings— Nodal  Lines  in  a  Vibrating  Plate — Stopped 
and  Open  Pipes — Organ  Pipes — Interference  of  Sound 
—Beats  in  Music— The  Voice— Stuttering,  -  -  20 

QUESTIONS, ...-30 


LIGHT. 

CHAPTER  I. 

Theories — Light  Proceeds  in  Straight  Lines — Definitions 
— Inversion  by  Rays  Passing  through  a  Small  Aper- 
ture— Shadow — Penumbra — Velocity  of  Light — Law 
of  Inverse  Squares — Measurement  of  Intensity  of 
Different  Sources  of  Light, 31 


6  CONTENTS. 

CHAPTER  II. 

PAGE 

Reflection,  Irregular  or  Scattered — Light  in  Itself  In- 
visible— Regular  Reflection,  Plain  Mirrors — Influence 
of  Obliquity — Formation  of  Images  by  Plain  Mirrors 
— Lateral  Inversion — Simple  Experiments,  Curious 
Facts  —  Polemoscope  —  Multiplication  of  Images — 
Kaleidoscope — Reflection  from  Curved  Mirrors- 
Spherical  Aberration — Caustics,  37 

CHAPTER  III. 

Refraction — Law  of  Refraction — Effects  of  Refraction — 
Refraction  always  Accompanied  by  Reflection  — 
Transparency — Opacity  of  Transparent  Mixtures — 
Total  Reflection — The  Limiting  Angle— Lenses,  Con- 
verging and  Diverging  —  Formation  of  Images  by 
Double  Convex  and  Double  Concave  Lenses — Camera 
Obscura — Magic  Lantern — Spherical  Aberration,  -  47 

CHAPTER  IV. 

The  Eye :  Its  Structure — Distinct  Vision — Punctum  Ccecum 
— Foramen  Centrale — Why  Objects  are  seen  Erect — 
Single  Vision — Adjustment  of  the  Eye  for  Different 
Distances — Long  and  Short  Sight — Spectacles — Size  of 
Objects— Visual  Angle — Persistence  of  Impressions — 
Irradiation — Stereoscope, CO 

CHAPTER  V. 

Medium  with  Parallel  Surfaces — Prisms :  Course  of  a  Ray 
through  a  Prism — Dispersion — Curious  Facts  as  to 
the  Solar  Spectrum — Recomposition  of  White  Light 
— Doctrine  of  Colours  —  Complementary  Colours  — 
Chromatic  Aberration, 71 

QUESTIONS,        -  78 


HEAT. 
CHAPTER  I. 

Nature  of  Heat— Heat  and  Cold— General  Effect  of  Heat- 
Expansion  of  Solids — Co-Efficient  of  Expansion — 
Practical  Applications — Breguet's  Metallic  Thermo- 
meter —  Gridiron  Pendulum  —  Exceptions  to  Expan- 
sion,   79 


CONTENTS.  « 

CHAPTER  II. 

PAGE 

Expansion  of  Liquids— Thermometer— Thermometric  Scales 
— Conversion  from  one  Scale  to  Another — Ebullition 
— Dependence  of  the  Boiling  Point  upon  External 
Pressure  —  Illustrations  —  Maximum  Density  of 
Water — Deportment  of  Water  in  Freezing — Effects  in 
Nature — Expansion  on  Solidification :  a  Property  not 
Peculiar  to  Water,  -------85 

CHAPTER  III. 

Expansion  of  Gases— Illustrations — Fire-Balloon—Con- 
stancy of  the  Co-efficient  of  Expansion — Physical 
Character  of  Carbonic  Acid  and  Sulphurous  Acid  Gases 
— Draft  of  Chimneys :  Ventilation — General  Character 
of  Winds — Trade  Winds — Land  and  Sea  Breezes,  ,  93 

CHAPTER  IV. 

Aqueous  Vapour :  Evaporation — Point  of  Saturation — Air 
Heated  by  Compression  and  Chilled  by  Expansion — 
Clouds:  Rain— Dew— Snow— Hail,  ....  100 

CHAPTER  V. 

Specific  Heat— Methods  of  Measuring  Specific  Heat  of 
Bodies — Table  of  Specific  Heats — Illustration— Influ- 
ence of  High  Specific  Heat  of  Water  011  Climate — 
Latent  Heat— Latent  Heat  of  Water  and  Steam— Cold 
of  Evaporation  —  Freezing  by  Evaporation  —  The 
Cryophorus,  - •  -105 

CHAPTER  VI. 

Convection— Conduction — Relative  Conductivity  of  Bodies 
— Illustrations — Effect  of  Mechanical  Texture — Cloth- 
ing—  Sensations  of  Heat  and  Cold — Combustion — 
Structure  of  a  Candle  Flame — Effect  of  Wire  Gauze — 
Bunsen  Lamp — Animal  Heat, 113 

CHAPTER  VII. 

Radiation  of  Heat :  Theory  of  Exchanges— Reflection  of 
Radiant  Heat — Radiating  Power  of  Bodies — Strange 
Effect  of  Close  Contact — Application  to  Common  Ex- 
perience— Absorbing  Power  of  Bodies — Reciprocity 
of  Radiation  and  Absorption — Refraction — Diather- 
mancy, ..,------  121 

QUESTIONS,        -       -        -       -       -       -        -  •     -        -      128 


CONTENTS. 


APPENDIX. 

FORMER  EXAMINATION  QUESTIONS,  WITH 
THEIR  SOLUTIONS. 

PAGE 

ACOUSTICS, 129 

LIGHT, 132 

HEAT,        ....  136 


ACOUSTICS. 


CHAPTER  I. 

1.  Object  of  Acoustics. — The  term  "acoustics"  is  derived 
from  a  Greek  verb  signifying  "to  hear."     It  is  applied  to 
designate  that   branch   of  science  which   treats  of  the 
phenomena  of  sound. 

2.  Cause  of  Sound. — The  immediate  cause  of  sound  is 
the  vibration  of  the  sounding  body.     If,  for  instance,  we 
take  a  glass  receiver,  and  holding  it  by  the  top,  strike  it 
with  a  wooden  mallet,  it  emits  a  clear  ringing  sound ;  and 
we  can  be  assured  of  the  fact  that  it  is  in  a  state  of  vibra- 
tion, by  observing  the  tremulous  motion  of  the  mallet 
when  allowed  to  rest  lightly  on  the  side  of  the  receiver — 
or  by  suspending  a  series  of  cork  balls  from  the  top  of 
the  receiver,  when  a  peculiar  dancing  motion  of  the  balls 
takes  place. 

3.  How  the  Air  is  Affected — Amplitude. — The  ques- 
tion arises,  in  what  way  is  the  air  affected  by  these  vibra- 
tions on  the  part  of  the  sonorous  body  1     The  particles  of 
air  in  the  immediate  vicinity  of  the  body  are  thrown  into 
a  forward,   and  thence  by  their  elasticity  into  a  back- 
ward motion,  passing  to  a  short  distance,  then  returning, 
and  so  on  successively ;   but  the  air  contiguous  to  this 
directly  affected  portion,  of  air  takes  up  the  impression, 
and  a  similar  motion  of  the  aerial  particles  takes  place ; 
in  like  manner  the  air  contiguous  to  this  second  affected 
portion  takes  up  the  impression ;  and  thus  the  original 
motion  is  transmitted  from  one  portion  of  air  to  another, 


10  ACOUSTICS. 

till  it'  gr^dt'.ally  diminishes,  and  eventually  dies  away  in 
the  distance.  The  air  therefore  is  moulded  into  a  series 
of:  aifected  portions,  in  each  of  which  the  aerial  particles 
have  but  a  limited  motion  to  and  fro.  That  motion,  it 
may  be  noticed,  takes  place  in  the  direction  in  which  the 
sound  is  propagated. 

The  amount  of  disturbance  thus  given  to  the  aerial 
particles  is  called  the  amplitude. 

4.  A  Sonorous  Wave — Wave-Length. — When  wind, 
coming  in  regular  gusts,  blows  over  a  field  of  standing 
grain,  a  wave-like  motion  is  seen  to  pass  over  it,  whilst 
the  heads  of  corn  perform  a  small  excursion  to  and  fro. 
In  some  parts  of  the  field  also,  the  heads  are  observed  to 
be  close  together,  and  in  other  parts  to  be  more  separated. 
Something  similar  is  believed  to  take  place  with  the 
aerial  particles  surrounding  a  sonorous  body;  whilst  these 
particles  move  a  small  distance  to  and  fro,  there  is  trans- 
mitted an  undulation  or  wave.  This  consists  of  two 
parts — a  condensation  and  a  rarefaction,  that  is,  one  part 
in  which  the  particles  of  air  are  compact,  and  another  in 
which  they  are  more  asunder.  The  distance  between  two 
consecutive  points  of  condensation  or  rarefaction,  as  from 
A  to  B,  or  C  to  D,  constitutes  the  length  of  the  sonorous 
wave  (fig.  1).  The  figure  shows  the  mode  of  propagation  of 


Fig.  1. 


VELOCITY   OF   SOUND — HOW   DETERMINED.  11 

a  sonorous  wave.  The  wave  gradually  enlarges  as  it  leaves 
the  bell,  whilst  at  the  same  time  the  motion  of  the  air 
particles  becomes  less  and  less,  just  as  in  the  case  of  the 
concentric  rings  which  are  observed  when  a  stone  is 
dropped  into  a  pool  of  still  water. 

The  sounding  body,  whatever  that  be,  is  continually 
sending  out  a  succession  of  such  waves.  These  sound- 
waves enter  our  ears,  affect  the  auditory  nerve,  and  pro- 
duce the  sensation  which  we  call  "sound." 

5.  Sound  is  not  Transmitted  through  a  Vacuum. — It 
is  essential  that  there  be  some  medium  for  the  transmis- 
sion of  sound.    The  ordinary  channel  of  conveyance  is  the 
air ;  but,  as  we  shall  afterwards  see,  there  are  other  sub- 
stances  which   convey  sound.      That   sound   cannot   be 
transmitted  through  a  vacuum  is  proved  by  the  ordinary 
experiment  of  ringing  a  bell  under  the  receiver  of  an  air- 
pump.     As  the  air  becomes  exhausted,  the  sound  of  the 
bell   gradually  diminishes   in   intensity   till   it   becomes 
almost   inaudible.      The  sound  indeed  would   be  quite 
inaudible  were  it  possible  to  make  a  complete  vacuum, 
and  were  we  able  to  dispense  with  the  supports  of  the  bell. 

This  experiment  proves  also  that  the  intensity  of  sound 
diminishes  with  the  density  of  the  air — a  fact  which  is 
well  known  to  those  who  ascend  lofty  mountains.  Thus 
it  is  said  that  at  the  top  of  Mont  Blanc  the  human  voice 
is  much  weakened,  and  that  the  report  of  a  pistol  resembles 
the  noise  of  a  boy's  pop-gun.  It  follows  from  such  obser- 
vations, that  the  loudest  noises  or  explosions  which  take 
place  on  the  earth's  surface,  could  not  be  heard  beyond 
the  limits  of  the  atmosphere. 

6.  Velocity  of  Sound — How  Determined — Sound  is 
not  conveyed  from  one  place  to  another  instantaneously — 
time  is  required  for  its  propagation.     This  is  abundantly 
evident  from  our  most  familiar  observation.     We  hear 
the  blows  of  a  hammer  at  a  distance  some  appreciable 
time   after   it   has   struck  the  object;   the  report  of  a 
distant  gun  reaches  our  ears  some  time  after  we  see  the 
flash. 


12  ACOUSTICS. 

The  velocity  of  sound  through  air,  at  a  given  tempera- 
ture, has  been  determined  in  the  following  manner : — 


Fig.  2. 

Let  the  distance  between  two  stations,  A  and  B,  be  care- 
fully measured.  Let  a  party  at  A  (fig.  2)  fire  a  gun,  whilst 
another  party  at  B  counts  the  number  of  seconds  between 
seeing  the  flash  and  hearing  the  report.  The  rate  at 
which  the  sound  travels  per  second  will  therefore  be 
found  by  dividing  the  distance  A  B  by  that  number.* 

From  a  series  of  very  careful  experiments  made  in 
different  countries,  it  appears  that  the  velocity  of  sound 
at  the  freezing  point  may  be  taken  at  1090  feet  per 
second,  and  that  the  increase  of  velocity  for  every  single 
degree  of  the  centigrade  thermometer  amounts  to  nearly 
two  feet. 

Solution  of  Questions. — There  are  certain  questions 
connected  with  the  velocity  of  sound  and  the  temperature, 
in  which  the  student  would  do  well  to  exercise  himself. 
The  nature  of  these  will  be  understood  from  the  following 
examples  : — 

Ex.  1. — Find  the  velocity  of  sound  through  air,  when 
the  temperature  is  25°  C. 

For  every  degree  centigrade  there  is  an  increase 
of  2  feet  in  the  velocity ;  therefore  for  25°,  an 
increase  of  25  x  2  or  50  feet ;  hence  the  velocity 
at  25°  C.  =  1090+  50  =  1140  feet.— ATM. 
Ex.  2. — Given  the  velocity  of  sound  to  be  1120  feet  per 
second,  what  is  the  temperature  of  the  air  ? 

Here,  if  we  deduct  1090/rom  the  given  velocity, 
we  obtain  the  amount  of  increase  above  the  velocity  at 
0°C. ;  hence  the  temperature  =  30  -H  2  =  15°C. — Ans. 

*  The  method,  it  will  be  observed,  is  founded  on  the  instan- 
taneous passage  of  light — a  doctrine  which  is  not,  strictly  speak- 
ing, true.  Light  travels,  however,  so  fast,  that  for  ordinary 
distances  the  time  required  for  its  transmission  is  virtually  inap- 
preciable. 


ELASTICITY   AND  DENSITY.  13 

Ex.  3. — An  interval  of  3  J  seconds  is  observed  to  elapse 
between  a  flash  of  lightning  and  the  peal  of  thunder, 
what  is  the  distance  of  the  electric  cloud,  the  tem- 
perature of  the  air  being  30°  C.  ? 

By  the  method  of  Ex.  1,  we  find  the  velocity 
of  sound  to  be  1150  feet;  hence  the  distance  — 
1150  x  3J  =  4025 /ee£.— Aiis. 

7.  Elasticity  and  Density — Influence  of  Tempera- 
ture.— The  two  conditions  that  must  be  taken  into  ac- 
count in  determining  the  velocity  of  propagation  of  a 
sonorous  wave  through  any  medium  are  its  elasticity  and 
density.  Speaking  more  strictly,  it  is  the  relation  the 
former  bears  to  the  latter,  which  determines  the  velocity 
of  propagation.  It  is  proved  mathematically  that  the 
velocity  is  directly  proportional  to  the  square  root  of  the 
elasticity,  and  inversely  proportional  to  the  square  root 
of  the  density. 

Now,  in  regard  to  the  atmosphere,  an  increase  of  tem- 
perature causes  a  decrease  in  the  density  of  the  air ;  and 
a  decrease  in  the  temperature  causes  an  increase  in  the 
density,  the  elasticity  remaining  the  same.  In  the  former 
case,  therefore,  sound  travels  faster,  and  in  the  latter  case 
slower. 

If  the  temperature,  however,  remain  constant — according 
to  Boyle's  or  Marriotte's  law* — the  elasticity  varies  in  the 
same  proportion  as  the  density ;  and  since  these  conditions 
are  directly  opposed  to  each  other,  it  follows  that  the 
velocity  of  sound  through  air  is,  on  this  supposition,  in  no 
way  affected.  Consequently,  there  is  no  effect  on  the 
velocity  of  sound,  unless  change  of  density  be  accompanied 
by  a  change  of  temperature. 

*  Boyle's  or  Marriotte's  "law  is  generally  enunciated  thus  :— 
"The  temperature  being  the  same,  the  volume  of  a  mass  of  air 
is  inversely  as  the  pressure  it  supports."  Thus,  if  we  have  a 
mass  of  air  occupying  1  cubic  foot,  at  the  ordinary  pressure  of 
the  atmosphere  (i.e.,  30  inches  of  mercury) — under  a  pressure  of 
2  atmospheres  it  will  occupy  -£  a  cubic  foot,  under  10  atmospheres 
^V  cubic  foot,  and  so  on.  It  follows,  of  course,  that  the  elasticity 
or  pressure  is  in  direct  proportion  to  the  density. 


14  ACOUSTICS. 

It  is  from  such  considerations  that  we  see  the  reason 
why  the  velocity  of  sound  is  not  affected  by  changes  in 
the  barometer,  but  only  by  changes  in  the  thermometer. 

8.  Changes  of  Temperature  in  a  Sonorous  Wave. — 
When  air  is  compressed  heat  is  evolved,  and  when 
rarefied  cold  is  produced;  therefore,  "in  the  condensed 
portion  of  a  sonorous  wave  the  air  is  above,  whilst  in  the 
rarefied  portion  of  the  wave  it  is  below  its  average  tem- 
perature. This  change  of  temperature,  produced  by  the 
passage  of  the  sound-wave  itself,  virtually  augments  the 
elasticity  of  the  air,  and  makes  the  velocity  of  sound 
about  one-sixth  greater  than  it  would  be  if  there  were  no 
change  of  temperature."  *  The  temperature  of  the  gene- 
ral mass  of  air,  however,  through  which  the  sound-waves 
pass  is  not  affected  by  these  changes.  Hence,  in  a  concert 
room  the  air  is  not  heated  by  the  passage  of  the  numerous 
sonorous  waves  which  are  constantly  proceeding  from  the 
orchestra. 


CHAPTER  II. 

9.  Intensity  of  Sound. — We  have  already  seen  that 
the  intensity  of  sound  depends  upon  the  density  of  the 
air  (Art.  5).  There  are  other  things  which  may  be  noticed 
in  regard  to  it. 

(1)  The  intensity  varies  inversely  as  the  square  of  the 
distance.     This  is  known  as  the  law  of  inverse  squares, 
and  is  the  same  as  regards  light  and  radiant  heat  (see 
Art.  32). 

(2)  The  intensity  depends  upon  the  density  of  the  air 
in  which  the  sound  is  generated,  and  not  on  that  in  which 
it  is  heard.     Thus,  if  two  observers  be  stationed  at  A 
and  B,  one  on  the  top  of  a  mountain  and  the  other  on  the 
plain  below,  at  equal  distances  from  a  gun  at  G  (fig.  3), 

*  Tyndall  on  Sound,  p.  46, 


PROPAGATION  OF  SOUND  THROUGH  OTHER  MEDIA.        15 

the  report  of  the  gun  will  have  the  same  loudness  to  each, 
though  the  air  at  A  is  more  rarefied  than  at  B.     If,  how- 


--1A. 


Fig.  3. 

ever,  there  be  two  guns,  giving  at  the  same  place  reports 
of  equal  loudness,  then  when  placed  at  A  and  B  respec- 
tively, to  an  observer  stationed  at  C  the  gun  at  B  will 
give  a  louder  report  than  the  gun  at  A. 

(3)  The  intensity  depends  upon  the  amplitude  (Art.  3). 
The  relation  between  the  two  is  more  strictly  expressed 
thus :  The  intensity  is  proportional  to  the  square  of  the 
amplitude. 

10.  Propagation  of  Sound  through  Other  Media. — 
Sound  is  not  only  transmitted  through  gaseous  bodies,  but 
also  through  liquids  and  solids.  The  velocity  through 
gases  is  comparatively  small;  it  is  greater  through  liquids, 
and  still  greater  through  solids. 

The  common  notion  that  the  velocity  through  a  medium 
is  in  proportion  to  its  density  is  quite  erroneous.  We 
must  take  into  account  the  relation  which  the  elasticity 
of  the  medium  bears  to  its  density  (Art.  7),  and  not 
either  element  in  itself.  Thus,  for  example,  if  we  take 
the  gases,  hydrogen  and  carbonic  acid,  we  find  that,  in 
comparison  with  the  velocity  through  air,  sound  -travels 
faster  through  hydrogen  and  slower  through  carbonic  acid 
— though  the  former  has  a  less  density,  and  the  latter  a 
greater  density  than  air.  The  true  reason  of  the  difference 
is,  therefore,  that  in  hydrogen  its  elasticity  as  compared 


16  ACOUSTICS. 

with  its  density  is  greater  than  in  the  case  of  air,  and  in 
carbonic  acid  less. 

In  liquids,  this  relation  is  higher  than  in  air ;  and  in 
solids,  still  higher.  Hence  the  velocity  of  sound  is  greater 
in  the  former,  and  still  greater  in  the  latter. 

The  following  table  gives  the  velocities  through  certain 
substances : — 

VELOCITY  OF  SOUND  THROUGH  DIFFERENT 

SUBSTANCES— (Ft.  per  Sec.). 

GASES.  LIQUIDS.  SOLIDS. 

Ash,...  15314 

Air, 1090(0°C)  Water  (fresh),  4708  (  8°C)  Oak,  ..12622 

Oxygen, . .  1040(0°C)  Alcohol, 4218  (20°C)  Gold,     5717  (20°C) 

Hydrogen  4164(0°C)  Solution  of  )  5132  (18°C)  Silver,   8553       ,, 
Carb.  Acid,  858(0°C)    Com.  Salt  j  Iron, . .  16822      , , 

It  appears  from  this  table  that  the  velocity  through 
water  is  more  than  four  times,  through  oak  eleven  times, 
and  through  iron  fifteen  times  the  velocity  through  air. 

The  readiness  with  which  solids  transmit  sound  is 
illustrated  by  several  familiar  facts.  The  slightest  scratch 
with  a  pin  at  one  end  of  an  iron  bar  is  distinctly  heard 
at  the  other.  By  placing  one  end  of  a  stick  on  the  lid  of 
a  boiling  kettle,  and  the  other  close  to  the  ear,  the  com- 
motion produced  in  the  water  is  rendered  very  audible. 
The  approach  of  a  body  of  cavalry  at  a  distance  can  be 
heard,  it  is  said,  by  applying  the  ear  to  the  ground. 

11.  Reflection  of  Sound. — When  a  wave  of  sound 
meets  an  obstacle  in  its  course  it  is  reflected.  The  law 
which  regulates  this  reflection  is  the  same  as  that  of  light 
(see  Art.  36). 

The  efficiency  of  tubes  to  convey  sound  depends  greatly 
on  reflection.  Biot  made  a  number  of  interesting  experi- 
ments with  the  water  pipes  at  Paris.  He  found  that 
with  a  tube,  upwards  of  3000  feet  in  length,  the  lowest 
whisper  could  be  heard.  "I  wished,"  says  Biot,  "to 
ascertain  the  lowest  pitch  at  which  the  voice  ceased  to  be 


ECHOES.  17 

heard ;  but  I  could  not  succeed.  Words  spoken  as  low 
as  when  one  whispers  into  the  ear  of  another  were  con- 
veyed and  appreciated,  and  I  concluded  that  the  only 
possibility  of  not  being  heard  was  not  to  speak  at  all." 

He  found  also  that  sounds  of  different  pitch  were 
conveyed  with  precisely  the  same  speed. 

The  reflection  of  sound  may  be  well  illustrated  by  the 
following  experiment : — 

B, 


Fig.  4. 

B  C  is  a  curved  metallic  reflector  (fig.  4)  placed  behind 
a  watch  at  A.  If  a  person  at  E  so  adjusts  himself  as  to 
have  his  ear  in  the  focus  of  the  sound-waves,  the  ticking 
of  the  watch  will  be  distinctly  heard.  A  funnel-shaped 
tube,  as  serving  to  entrap  as  many  waves  as  possible,  is 
of  advantage  in  the  experiment. 

The  ear-trumpet,  the  speaking-trumpet,  whispering  gal- 
leries, etc.,  all  owe  their  action  to  the  reflection  of  sound. 
Among  the  ancients  a  notorious  instance  of  a  sound- 
collecting  surface  was  the  "  Ear  of  Dionysius"  in  the 
dungeons  of  Syracuse.  The  roof  of  the  prison  was  so 
constructed  as  to  transmit  the  words  and  even  the  whis- 
pers of  the  unhappy  victims  there  confined,  to  the  ear  of 
the  tyrant  through  a  narrow  passage  cut  through  the 
solid  rock. 

12.  Echoes. — An  echo  is  also  a  result  of  the  reflection 
of  sound.     But  it  becomes  necessary  to  enquire  into  the. 
precise  circumstances  under  which  it  is  produced, 
SE  B 


18  ACOUSTICS. 

For  this  purpose  we  must  keep  in  view  two  things : 
(1)  the  velocity  of  sound;  and  (2)  the  fact  that  the  ear 
cannot  appreciate  two  sounds  distinctly,  unless  an  interval 
of  one-tenth  of  a  second  elapse  between  them.  Now, 
taking  the  standard  temperature  of  62°  Fahrenheit,  sound 
travels  at  the  rate  of  1 125  feet  per  second;  in  one-tenth  of 
a  second,  therefore,  it  will  travel  over  112  J  feet.  Hence 
the  least  distance  at  which  a  person  must  place  himself 
from  the  reflecting  surface,  so  as  to  make  an  echo  possible, 
must  be  about  56  feet.  Within  this  distance  the  reflected 
sound  blends  with  the  original,  causing  a  certain  amount 
of  enforcement,  but  no  echo.  On  the  other  hand,  as  this 
distance  is  exceeded,  the  echo  becomes  more  and  more 
distinct. 

Echoes  are  met  with  in  all  parts  of  the  world,  differing 
much  in  their  distinctness  and  character.  One  of  the 
best  echoes  to  be  found  in  Britain  is  in  Woodstock  Park. 
It  is  said  to  repeat  seventeen  syllables  by  day  and  twenty 
by  night.  At  a  villa  near  Milan  there  is  one  which 
is  said  to  repeat  a  shout  thirty  times. 

The  repetition  which  is  met  with  in  such  cases  results 
from  the  repeated  reflection  of  the  original  sound  by 
different  obstacles,  each  repetition  becoming  fainter  and 
fainter,  till  it  dies  away  in  the  distance. 

The  rolling  of  thunder  is  undoubtedly  due  in  part  to 
the  echoes  caused  by  the  presence  of  prominent  objects, 
such  as  houses  and  mountains,  and  to  reflection  amongst 
the  clouds.  It  is  also  believed  to  be  owing  to  the  diiferent 


Fig.  5. 

aerial  agitations  in  the  track  of  the  lightning  reaching  the 
ear  at  different  times. 


STRUCTURE   OF   THE   EAR. 


19 


13.  Refraction  of  Sound. — Sound,  like  light,  can  also 
be  refracted,  that  is,  bent  out  of  its  course  by  the  inter- 
position of  some  medium.     This  is  effected  in  the  case  of 
sound  by  filling  a  thin  india-rubber  balloon  with  carbonic 
acid  gas,  and  placing  a  watch,  for  example,  at  A,  as  in 
fig.  5.     The  sound-waves  are  refracted  by  the  balloon, 
and  concentrated  in  a  focus  at  B,  where  the  ticking  of 
the  watch  may  be  distinctly  heard. 

14.  Structure  of  the  Ear — Range  of  Appreciation  for 
Musical  Sounds. — The  human  ear  may  be  described  as 
consisting  of  three  parts — the  outer  ear,  the  middle  ear, 
and  the  labyrinth.     The  accompanying  diagram  exhibits 
the  different  parts : — 


Fig.  G. 

1 — The  concha.  2 — The  meatus.  3 — The  tympanum 
or  drum;  this  closes  the  outer  ear.  4,  5,  6,  7 — A  series 
of  bones  which  transmit  the  impressions  made  on  the 
tympanum,  called  respectively  the  malleus,  incus}  os  orbi- 


20  ACOUSTICS. 

cularis,  and  stapes.  8, 8 — The  tympanic  cavity  or  middle 
ear.  9 — The  Eustachian  tube,  leading  into  the  back  of 
the  mouth,  by  which  the  air  in  the  tympanic  cavity  is 
kept  of  the  same  density  as  that  of  the  external  atmo- 
sphere, giving  the  tympanum  therefore  perfect  freedom 
of  motion.  10,  10,  10 — The  labyrinth,  throughout  which 
the  auditory  nerve  is  distributed. 

The  sonorous  waves,  entering  the  outer  ear,  throw  the 
tympanic  membrane  into  a  state  of  vibration.  These 
vibrations  are  transmitted  across  the  middle  ear  through 
the  series  of  bones  towards  the  labyrinth;  there  they 
affect  the  auditory  nerve,  and  produce  the  sensation  of 
hearing. 

An  ordinary  musical  ear  can  appreciate  sounds  arising 
from  16  vibrations*  per  second  up  to  38,000,  that  is, 
a  range  of  about  11  octaves,  f  How  is  this  accommo- 
dation of  the  organ  effected?  Looking  to  the  anatomy 
of  the  tympanum,  it  appears  that  this  adaptation  to 
different  rates  of  vibration  is  effected  by  means  of 
slender  muscles,  which  tighten  or  slacken  the  membrane 
according  as  the  vibrations  which  fall  upon  it  are  quick 
or  slow,  thereby  tuning  it,  as  it  were,  to  the  proper 
discharge  of  its  wonderful  office. 


CHAPTER  III. 

15.  Physical  Difference  between  a  Musical  Sound 
and  Noise. — The  sensation  we  experience  at  once  indi- 
cates the  difference  between  a  musical  sound  and  noise. 
But  what  is  the  real  physical  cause  of  the  difference  1  It 
is  this :  a  musical  sound  is  produced  by  periodic  impulses 

*  By  a  vibration  in  this  country  is  meant  an  excursion  of  the 
vibrating  body  to  and  fro,  not  a  movement  backward  or  forward, 
but  both  together. 

t  The  practical  range  of  musical  sounds  is  from  40  to  4000 
vibrations  per  second, 


METHOD  OF  DETERMINING  THE  NUMBER  OF  VIBRATIONS.  21 

given  to  the  air,  that  is,  by  impulses  which  succeed  each 
other  after  perfectly  regular  intervals  of  time.  A  noise, 
on  the  other  hand,  is  produced  by  impulses  which  do  not 
succeed  each  other  regularly.  The  vibrations  of  a  tuning- 
fork,  and  the  confused  mingled  noise  of  the  street,  are 
familiar  illustrations. 

It  is  sometimes  difficult,  however,  to  draw  the  exact 
line  of  demarcation,  as,  for  example,  in  the  case  of  a  boy 
running  a  stick  along  a  railing,  or  in  the  clink  of  the 
wheels  of  a  railway  carriage  when  it  is  moving  rapidly. 

16.  Pitch,  Intensity,  and  Quality  of  Musical  Sounds. 
— Some  sounds  are  said  to  be  "  grave,"  others  "  acute." 
This  difference  in  the  character  of  musical  sounds  depends 
upon  what  is  called  pitch,  that  is,  upon  the  number  of 
vibrations  performed  in  one  second.     Thus,  if  we  have  two 
tuning-forks  giving  respectively  280  and  420  vibrations 
per  second,  the  note  from  the  former  is  of  a  lower  pitch 
than  the  note  from  the  latter. 

Intensity  arises  from  difference  in  the  amplitude  of  the 
vibrations.  The  same  sound  or  note  of  a  certain  pitch 
may  have  different  degrees  of  loudness  or  intensity,  accord- 
ing to  the  range  of  vibration  given  to  the  sounding  body. 

Quality  (perhaps  better  expressed  by  the  French  word 
timbre),  is  the  distinction  which  may  be  drawn  between 
two  notes  of  the  same  pitch  and  intensity,  when  sounded 
on  different  instruments,  as,  for  example,  on  the  violin 
and  flute.  It  is  believed  to  be  due  to  certain  subsidiary 
notes  or  "harmonics,"  as  they  are  termed,  accompany- 
ing, or  being  blended  with,  the  original  note. 

17.  Method  of  Determining  the  Number  of  Vibra- 
tions.— One  of  the  simplest  methods  of  determining  the 
number  of  vibrations  of  a  musical  sound,  is  by  means  of 
Savart's  apparatus.     The  machine  consists  of  two  wheels, 
A  and  B,  fixed  in  a  wooden  frame  (fig.  7),  the  smaller 
having  a  certain  number   of  teeth  in  the  rim.     They 
are  so  adjusted,  that  B  is  made  to  revolve  with  great 
rapidity,  its  teeth  hitting  upon  a  card  E  fixed  near  it.    The 
number  of  revolutions  is  indicated  by  a  counter  attached 


ACOUSTICS. 


to  the  axis  at  H.     The  method  of  procedure  will  be 
understood  by  an  example.      The  number  of  vibrations 


:SF 


Fig.  7. 


of  a  tuning-fork,  C,  mounted  upon  a  sounding-box,  is 
required.  We  should  first  sound  the  fork,  and  gradu- 
ally increase  the  revolution  of  the  wheel,  B,  until  the 
note  emitted  by  the  card  corresponds  to  that  of  the  fork. 
We  should  then  keep  them  in  unison  for  a  certain  number 
of  seconds,  say  ten.  Now,  if  we  suppose  that  there  are 
100  teeth  in  the  wheel,  B,  and  that  during  the  ten  seconds 
the  counter  indicates  fifty  revolutions,  we  shall  then  have 
5000  as  the  number  of  shocks  or  vibrations  given  to  the 
card  in  that  time.  Hence  5000  divided  by  10,  or  500, 
will  be  the  number  of  vibrations  which  the  tuning-fork 
performs  per  second. 

Solution  of  Questions.  —  Given  the  number  of 
vibrations  of  a  musical  note,  we  can  easily  find  the 
length  of  sound-wave  it  produces.  Conversely,  given  the 
length  of  sound-wave,  we  can  find  the  number  of  vibra- 
tions. 

Ex.  1. — A  musical  note  gives  300  vibrations  per  second, 
find  the  length  of  the  sound-tvave  it  produces. 

Taking  the  velocity  of  sound  at  62°  Fahrenheit, 
we  have  the  first  sound-wave  sent  off,  travelling 


SONOMETER.  23 

over  1125  in  one  second;  but  the  note  in  the 
example  gives  300  vibrations,  or  sends  off  300 
sound-waves  in  that  time  ;  hence  1125  v  300  =  Zft. 
9  in.  =  length  of  one  wave. — Ans. 

Ex.  2. — The  length  of  sound-wave  which  a  musical  note 
gives  is  4|-  feet,  find  its  number  of  vibrations. 

Here  it  is  evident  we  have  only  to  divide  1125 
feet  by  the  wave-length;  hence  1 1 25 -j- 4^  =  250  = 
number  of  vibrations. — Ans. 

19.  Sonometer — Influence  of  Sound-Boards — Reson- 
ance.— The  sonometer  is  an  instrument  used  to  illustrate 
the  vibrations  of  strings,  and  the  laws  which  regulate 
these  vibrations.  A  convenient  form  of  it  is  represented 
in  fig.  8.  Each  string  is  supported  on  two  bridges,  ono 


Fig.  8. 

of  which  is  movable,  and  by  means  of  which,  therefore, 
any  part  of  the  strings  can  be  sounded.  At  one  end  there 
is  a  hollow  box  or  sound-board  A,  which  resounds  under  the 
influence  of  the  vibrating  strings,  and  thus  very  much 
enforces  the  sound.  We  have  a  similar  effect  in  all  our 
stringed  instruments — violins,  harps,  pianos,  etc.;  they 
owe  their  richness  and  fulness  of  tone  to  the  reverberation 
of  the  materials  which  support  the  strings.  This  effect 
is  known  as  resonance. 


ACOUSTICS. 


We  may  have  resonance  also  from  a  column  of  air. 
Thus,  if  a  tuning-fork  be 
held  over  the  mouth  of  a 
glass  jar  (fig.  9),  the  sound 
is  intensified.  The  height 
of  the  jar,  which  gives  the 
maximum  resonance,  is 
found  by  experiment  to 
be  one -fourth  of  the 
length  of  the  sound-wave 
which  the  fork  pro- 
duces. 

20.  Nodes  and  Ventral 
Segments. — If  a  jerk  or 
pulse  be  sent  along  a  string 


fixed  at  one  end,  it  is  re- 


Fig.  0. 


fleeted  at  the  fixed  end,  and  returns  to  the  hand.  The  time 
it  requires  to  travel  to  the  fixed  end  and  back,  is  the  same 
as  that  required  by  the  whole  string  to  execute  a  complete 
vibration.  If  a  series  of  jerks  be  sent  in  succession  along 
the  string,  the  direct  and  reflected  pulses  meet,  and  by 
their  coalescence  divide  the  string  into  a  series  of  vibra- 
ting parts,  called  ventral  segments,  which  are  separated 
from  each  other  by  points  of  apparent  rest,  called  nodes. 
This  may  be  well  shown  by  taking  a  few  yards  of  common 
window  cord,  as  flexible  as  possible,  fixing  it  at  one  end, 
and  after  a  succession  of  jerks  has  been  given  to  it  at  the 
other  end,  tightening  the  string  slightly.  It  may  divide 
itself,  as  in  fig.  10.  AB,  BC,  CD  are  the  ventral  seg- 
ments, B  and  C  the  nodes. 


Fig.  10. 

The  number  of  ventral    segments    depends    upon  the 
rapidity  with  which  the  jerks  have  been  imparted. 

This  division  of  a  string  may  also  be  illustrated  by  the 


KODAL  LINES   IN  A  VIBRATING   PLATE.  25 

sonometer.  Thus,  if  we  place  the  bridge  at  a  point,  such 
that  AB  is  one-third  of  the  length  of  the  string  (fig.  8), 
and  draw  the  bow  across  that  part,  the  remainder  of  the 
string  will  divide  itself  into  two  parts ;  that  is,  there  will 
be  two  ventral  segments  separated  by  a  node.  A  simple 
method  of  proving  this  is  to  take  three  small  pieces  of 
cardboard,  and  place  them  at  the  points  C,  D,  E.  When 
A  B  is  sounded,  the  middle  one  will  remain  comparatively 
unaffected,  whilst  the  other  two  will  be  so  much  disturbed 
by  the  vibration  as  to  be  thrown  off. 

21.  Laws  of  the  Vibration  of  Strings. — The  transverse 
vibration  of  strings  is  dependent  upon  four  things;  viz., 
length,  thickness,  tension,  and  density.  Accordingly, 
there  are  four  laws  which  regulate  the  vibrations.  They 
are  as  follow  : — 

(1)  The  number  of  vibrations  of  a  string  is  inversely  as 
its  length. 

(2)  The  number  of  vibrations  is  inversely  as  its  dia- 
meter. 

(3)  The  number  of  vibrations  is  directly  proportional 
to  the  square  root  of  the  stretching  force. 

(4)  The  number  of  vibrations  is  inversely  proportional 
to  the  square  root  of  its  density. 

Hence  half  of  a  string  gives  double  the  number  of  vibra- 
tions— the  note  it  produces  is  the  octave  to  the  original. 
Hence,  also,  if  we  have  two  similar  strings,  the  one  twice 
as  long  as  the  other  but  only  half  the  diameter,  these 
strings  will  give  the  same  note. 

'22.  Nodal  Lines  in  a  Vibrating  Plate. — We  have 
not  only  nodal  points  in  a  vibrating  string,  but  we  may 
have  nodal  lines  in  a  vibrating  plate. 

Thus,  if  we  take  a  metallic  plate  (fig.  1*1),  and  sprinkle 
sand  uniformly  over  it,  by  drawing  a  fiddle-bow  across 
the  middle  point  of  one  of  its  sides,  the  sand  collects 
along  the  diagonal  lines,  completely  leaving  the  other 
parts  of  the  plate,  which  we  infer  are  thus  thrown  into  a 
state  of  rapid  vibration.  If  the  bow  be  drawn  across  a 
point  near  one  of  the  corners,  the  sand  is  arranged 


26  ACOUSTICS. 

along  the  lines  joining  the  middle  points  of  the  opposite 
sides. 


Tig.  11. 

23.  Stopped  and  Open  Pipes. — We  have  now  to  look 
at  the  vibration  of  columns  of  air  in  pipes.  It  is  the 
column  of  air  itself,  in  such  cases, 
which  is  the  cause  of  the  sound, 
and  not  the  material  of  which  the 
pipe  is  constructed. 

In  both  stopped  and  open  pipes 
the  number  of  vibrations  is  in- 
versely proportional  to  the  length 
of  the  pipe.  This  may  be  illus- 
trated by  taking  three  glass  tubes 
(fig.  12),  A,B,C,  say  16  in.,  8  in., 
Fig.  12.  and  4  in.  long,  respectively,  and 

blowing    across   their    open    ends. 
Whilst  A  gives  a  certain  note,  B  gives  the  octave,  and 


ORGAN   PIPES. 


27 


C  the  octave  to  B.  In  the  case  of  open  tubes,  it  is  diffi- 
cult to  elicit  the  notes  in  this  manner,  and  an  arrange- 
ment such  as  obtains  in  an  organ  pipe  must  be  adopted. 

24.  Organ  Pipes— State  of  the  Air  in  Stopped  and 
Open  Pipes. — The  manner  in  which  the  column  of  air  is 
made  to  vibrate  in  an  organ  pipe  will  be  understood  from 

%  13.  S 

The  air,  urged  through  the  tube  A,  is  led 
through  the  narrow  passage  A  B,  and  made  to 
play  upon  the  thin  edge  of  the  pipe  at  the  em- 
bouchure C.  It  produces  there  a  kind  of  flutter, 
some  pulse  of  which  is  raised  by  the  resonance  of 
the  aerial  column  inside  to  a  musical  sound,  and 
thus  the  pipe  "  speaks."  In  an  open  pipe  there 
is  a  flexible  metallic  tongue,  which,  by  being 
moved  up  or  down,  serves  the  purpose  of  tuning 
it.  In  a  stopped  pipe  there  is  a  plug  or  piston 
at  the  top,  which  may  be  moved  out  or  in. 

If  a  stopped  pipe  and  an  open  one  of  the  same 
length  be  sounded,  the  note  emitted  by  the 
former  is  an  octave  below  the  latter ;  hence,  to 
have  the  same  note  with  a  stopped  pipe  as  with 
an  open  one,  the  former  must  be  half  the 
length  of  the  latter. 

When  a  stopped  pipe  gives  its  fundamental 
note,*  the  column  of  air  inside  is  undivided  by 
a  node — the  stopped  end  is  a  node  and  the  open 
end  the  middle  of  a  ventral  segment.  In  an  open 
pipe,  again,  the  column  is  divided  by  a  node  at 
its  centre — each  end  being  the  middle  of  a  ventral 
segment. 

The   length    of  the    sonorous   wave    of  the  Fig.  13. 
note  produced  in  a  stopped  pipe  is  four  times  the  length 
of  the  pipe,  and  in  an  open  one  twice  the  length. 

*  By  the  fundamental  note  of  a  pipe  is  meant  the  lowest  note 
which  can  be  drawn  from  it.  Harmonics  may  be  drawn  from  a 
pipe  by  increasing  the  intensity  of  the  current  of  air 
through  it. 


ACOUSTICS. 


If  hydrogen  and  carbonic  acid  gas  be  urged  in  succession 
through  an  organ  pipe,  the  note  produced  in  the  former 
case  is  of  higher  pitch,  and  in  the  latter  case  of  lower 
pitch,  than  when  air  is  urged  through  the  pipe.  This  results 
from  the  comparative  velocities  of  sound  in  these  gases. 

25.  Interference  of  Sound  Waves — Beats  in  Music. 
— If  a  tuning-fork,  which  is  held  over  the  mouth  of  a 

resonant  jar,  be  gradu- 
ally moved  towards  the 
side  its  sound  becomes 
enfeebled,  and  almost 
disappears,  when  in  the 
position  represented  in 
tig.  14.  This  is  due  to 
the  sound-waves  pro- 
ceeding from  the  prongs 
of  the  fork  neutralizing 
each  other  —  an  effect 
known  as  interference. 
A  similar  effect  takes 
place  if  the  fork  be  held 
Fig.  14.  close  to  the  ear,  and  slow- 

ly turned  on  its  axis. 

When  two  sonorous  bodies,  whose  periods  of  vibration 
slightly  differ,  emit  sound  together,  a  series  of  alternate 
reinforcements  and  diminutions  of  the  sound  are  observed, 
called  in  music  beats.  They  are  caused  by  the  sonorous 
waves  of  the  two  bodies  at  one  time  conspiring,  and  at 
another  time  being  opposed,  in  their  action  on  each 
other — a  result,  therefore,  of  interference. 

These  beats  may  be  well  heard  by  sounding  a  low  note 
and  its  sharp  on  a  piano. 

It  may  be  proved  that  the  number  of  beats  per  second 
is  just  equal  to  the  difference  between  the  rates  of  vibra- 
tion of  the  two  notes.  Concord  or  harmony  in  music 
results  from  the  frequency  in  the  coincidence  or  coales- 
cence of  the  vibrations  j  discord,  on  the  other  hand,  from 
the  unfrequency  with  which  this  occurs. 


THE  VOICE — STUTTERING. 


29 


26.  The  Voice — Stuttering. — The  top  of  the  wind- 
pipe or  trachea  is  closed  by  two  membranes  placed  edge 
to  edge,  leaving  only  a  small  slit  or  opening  between 
them,  called  the  glottis.  These  membranes  are  acted 
upon  by  elastic  bands,  called  the  vocal  chords,  which  are 
relaxed  or  tightened  at  will.  There  is  a  flap  or  lid,  termed 
the  epiglottis  (fig.  15),  which  accurately  covers  the  glottis. 
The  food,  in  its  passage  into 
the  gullet,  presses  upon  this  lid 
and  keeps  it  close  upon  the 
aperture  until  the  food  has 
passed;  when,  from  its  elastic- 
ity, it  rises  and  allows  respira- 
tion to  go  on.  When  we  are 
breathing,  but  not  speaking,  the 
membranes  of  the  glottis  are 
in  a  state  of  relaxation,  and  the 
air  in  its  exit  from  the  lungs 
has  too  little  force  to  cause  them 
to  vibrate;  in  these  circum- 
stances there  is  no  sound,  no 
voice.  When  we  wish  to  speak,  l&' 

no  sooner  does  the  volition  exist  than  the  vocal  chords 
brace  up  the  membranes  to  the  necessary  tension;  the 
lungs  then  doing  their  duty  send  a  blast  of  air  through 
the  glottis,  throw  the  membranes  into  vibration,  and  thus 
sound  or  voice  is  produced. 

"  The  sweetness  and  smoothness  of  the  voice  depend  on 
the  perfect  closure  of  the  slit  of  the  glottis,  at  regular 
interval's,  during  the  vibration.  .  .  .  Through  the  agency 
of  the  mouth  we  can  mix  together  the  fundamental  tone 
and  the  overtones  (harmonics)  of  the  voice  in  different 
proportions,  and  the  different  vowel  sounds  are  due  to 
different  admixtures  of  this  kind."  * 

Stuttering  in  speech  is  believed  to  arise  from  some 
inability  on  the  part  of  the  stutterer  to  open  his  glottis. 
It  has  been  recommended  to  such  persons  when  speaking 
*  Tynaall  on  found,  pp.  190-199, 


30  ACOUSTICS. 

to  drawl  out  their  conversation  in  a  continuous  sound, 
so  as  to  prevent  their  glottis  from  closing.  Hence  we 
find  that  stutterers  can  often  sing  well,  and  without  the 
least  interruption;  for  the  tune  being  continued  the 
glottis  does  not  close,  and  there  is  consequently  no  hesita- 
tion. Many  stutterers  can  also  read  poetry  well,  or  any 
declamatory  composition  in  which  the  sound  is  almost  as 
much  sustained  as  in  singing. 


QUESTIONS. 

1.  What  is  the  velocity  of  sound  in  air  at  the  freezing  point  ? 
Calculate  the  velocity  when  the  temperature  is  10°  C. 

Ans.  (1)  1090;  (2)  1110. 

2.  How  is  the  velocity  of  sound  affected  (1)  by  a  change  of 
density?  and  (2)  by  a  change  of  elasticity?    Why  is  the  velocity 
through  a  solid  greater  than  through  a  liquid,  and  still  greater 
than  through  a  gas  ? 

3.  Describe  a  method  of  determining  the  number  of  vibrations 
of  a  sonorous  body. 

4.  Describe  an  experiment  to  prove  that  sound  cannot  pass 
through  a  vacuum. 

5.  Distinguish  between  a  musical  sound  and  a  noise.    On  what 
do  the  pitch,  intensity,  and  quality  of  musical  sounds  depend  ? 

6.  A  sonorous  body  gives  wave-lengths  of  3|  feet,  how  many 
vibrations  does  it  execute  in  one  second  (temp.  =  15° C.)  ? 

Ans.  320. 

7.  A  and  B  are  two  similar  strings  stretched  with  the  same 
force  ;  A  has  twice  the  length  of  B,  but  only  half  the  diameter. 
Compare  their  rates  of  vibration.  Ans.  Equal. 

8.  What  is  the  length  of  the  sonorous  wave  produced  (1)  by  a 
stopped  pipe  2  feet  long,  and  (2)  by  an  open  pipe  of  the  same 
length,  each  sounding  its  fundamental  note  ? 

Ans.  (1)8  feet,  (2)  4  feet. 

9.  How  does  an  organ  pipe  "speak?"    What  is  the  state  of 
the  air  inside  (1)  an  open,  and  (2)  a  stopped  pipe,  when  each 
gives  its  fundamental  note. 

10.  What  is  the  cause  of  beats  in  music  ?    How  many  beats 
per  second  would  occur  when  two  tuning  forks  are  sounded  to- 
gether, which  give  300  and  310  vibrations  per  second  respectively? 


LIGHT, 


CHAPTER  I. 

27.  Theories  in  Regard  to  Light.—  There  are  two 
main  theories  which  have  been  proposed  in  reference  to 
the  nature  of  light.      One  of  these  is  termed  the  emission 
or  corpuscular  theory,  the  other,  the  undulatory  theory. 

According  to  the  former,  light  consists  in  the  actual 
emanation  of  luminous  particles  from  the  luminous  body; 
that  these  particles  are  of  inconceivable  minuteness, 
and  by  their  actually  striking  upon  our  eyes,  that  they 
excite  the  sensation  of  vision,  in  the  same  way  as  the  fine 
particles  of  any  odorous  substance,  by  entering  our  nos- 
trils, excite  the  sense  of  smell. 

In  the  latter  hypothesis,  it  is  assumed  that  all  bodies, 
as  well  as  all  space,  are  pervaded  with  an  extremely  thin 
and  highly  elastic  fluid  .called  ether ;  that  light  is  caused 
by  a  vibratory  motion  imparted  to  the  molecules  of  this 
substance,  in  consequence  of  which  a  series  of  undula- 
tions or  waves  are  produced;  and  that  it  is  by  the  suc- 
cessive shocks  of  these  minute  waves  upon  our  eyes  that 
vision  is  excited,  somewhat  in  the  same  manner  as  the 
waves  of  sound,  proceeding  from  a  sonorous  body,  by 
entering  our  ears,  excite  the  sensation  of  sound. 

The  undulatory  theory,  from  its  perfect  competency  to 
explain  all  the  varied  phenomena  connected  with  light, 
is  the  one  more  generally  adopted  by  modern  physicists. 

28.  Light  Proceeds  in  Straight  Lines— Definitions. — 
That  light  is  propagated  in  straight  lines  is  manifest  from 
various  facts.     We  cannot  see  round  a  corner.     If  we 


32 


LIGHT. 


hold  an  opaque  object  in  front  of  a  candle,  we  fail  to  see 
the  candle.  If  a  small  hole  be  made  in  the  shutter  of  a 
darkened  room,  the  track  of  a  beam  of  light,  as  marked 
out  by  the  floating  particles  of  dust,  is  observed  to  be 
perfectly  straight. 

Towards  sunset,  when  the  sun  is  concealed  by  a  cloud 
(fig.  17),  straight  beams  of  light  are  observed  to  radiate 
from  him  in  all  directions,  and  to  shed  a  glowing  effect 
upon  a  surrounding  landscape. 


Fig.  17. 

A  ray  of  light  is  an  indefinitely  small  portion  of  light 
mere  line  in  thickness.  An  assemblage  of  such  rays 
is  termed  a  pencil  or  beam  of  light;  when  the  rays  pro- 
ceed in  parallel  directions,  the  pencil  is  said  to  be  parallel; 
when  they  proceed  in  all  directions,  it  is  divergent,  and 
when  they  converge  towards  a  point,  it  is  convergent. 
Parallel  and  convergent  beams  are  met  with  in  optical 
instruments;  divergent  beams  are  the  most  common,  and 
are  such  as  proceed  from  any  luminous  body, 


SHADOW — PENUMBRA. 


33 


29.  Inversion  of  an  Object  by  Rays  Passing  through 
a  Small  Aperture. — This  is  a  necessary  consequence  of 
the  rectilinear  propagation  of  light.  Thus,  let  a  small 
aperture  be  made  in  the  shutter  C  of  a  darkened  room 


(fig.  18),  an  inverted  image  of  the  external  object  A  B 
will  be  formed  upon  the  opposite  wall  at  D,  the  inver- 
sion being  caused  by  the  crossing  of  the  rays.  The 
shape  of  the  image,  in  such  a  case,  is  precisely  the  same 
as  that  of  the  object,  and  is  independent  of  the  form  of 
the  aperture. 

30.    Shadow — Penumbra. — The    shadow    which    an 
opaque  body  casts  behind  it  when  exposed  to  light  is 


Fig.  19. 

also  a  consequence  of  the  same  principle.     In  the  case 
of  a  luminous  point,  it  is  easy  to  define  or  mark  off  the 
8  E  c 


34  LIGHT. 

shadow.  If,  however,  we  have  a  luminous  body  besides 
the  true  shadow,  there  is  produced  also  a  partial  shadow 
or  penumbra,  as  it  is  called.  Thus,  if  P  be  a  luminous 
point  (fig.  19),  and  B  an  opaque  spherical  body,  the  shadow 
which  it  casts  behind  is  marked  off  by  the  black  part  of  the 
diagram,  and  shows  itself  on  the  screen,  E  F,  as  a  dark 
circular  disc,  having  a  diameter  C  D.  But  if  A  G  be 
the  luminous  body,  the  shadow  B  C  D  H  is  fringed  with 
the  lighter  spaces  B  C  E,  H  D  F,  which  are  exhibited  on 
the  screen  as  a  shady  circular  ring  surrounding  the  disc 
C  D.  This  constitutes  the  penumbra. 

In  a  total  eclipse  of  the  sun,  the  region  of  the  earth 
where  it  occurs  is  in  the  shadow  cast  by  the  moon;  the 
tract  of  country,  again,  from  which  a  partial  eclipse  is 
observed,  is  in  the  penumbra.  Beyond  the  penumbra 
there  is  no  eclipse  visible. 

31.  Velocity  of  Light. — The  transmission  of  light 
from  one  point  to  another  is  not  instantaneous.  The 
rate  of  transmission,  however,  is  so  great,  that  for  any 
distance  on  the  earth's  surface  ordinary  observation  can- 
not detect  any  appreciable  interval  of  time  between  the 


Fig.  20. 

occurrence  of  the  luminous  phenomenon  and  its  reaching 
the  eye.  The  velocity  of  light  was  first  established  by 
Rcemer,  a  Danish  astronomer,  in  1675.  He  deduced 
it  from  observations  on  the  first  satellite  of  Jupiter. 


LAW  OF  INVERSE  SQUARES.  35 

Fig.  20  will  show  the  nature  of  the  investigation.  By 
a  series  of  careful  observations,  he  found  that  the 
eclipse  of  the  satellite  S  took  place  about  15  minutes 
sooner  when  the  earth  was  at  E  nearest  to  Jupiter,  than 
when  at  E'  farthest  away  from  him.  This  difference  of 
time  he  very  properly  accounted  for  thus :  that  the  last 
glimpse  of  light  sent  off  from  the  satellite  previous  to  its 
passing  into  Jupiter's  shadow  was  delayed  this  interval 
in  traversing  the  earth's  orbit,  that,  in  fact,  the  light 
took  15  minutes  to  cross  from  E  to  E'.  In  this  way 
ll'.mner  determined  the  velocity  of  light  to  be  192,500"' 
miles  per  second. 

This  prodigious  velocity  will  be  more  readily  conceived 
of,  when  we  state,  that  whilst  light  takes  about  7  min- 
utes to  travel  from  the  sun  to  the  earth,  a  cannon  ball 
retaining  its  initial  velocity  of  1600  feet  per  second, 
would  perform  the  same  journey  in  17  years,  and  an 
express  train  going  at  the  rate  of  40  miles  an  hour  in 
265  years. 

Notwithstanding  this  enormous  speed,  the  nearest 
stars  are  so  far  off  that  their  light  takes  between  three 
and  four  years  to  reach  us;  and  it  has  been  presumed  that 
the  more  distant  stars  in  the  universe  are  so  remote,  that 
the  light  from  them  may  take  hundreds  or  even  thou- 
sands of  years  to  reach  our  globe. 

32.  Law  of  Inverse  Squares. — The  intensity  of  light 
diminishes  with  the  distance  from  the  luminous  body 
according  to  the  same  law  as  that  in  regard  to  sound 
(Art.  9).  It  is  well  illustrated  by  the  accompanying 
diagram  (fig.  21). 

Let  A  B,  C  D,  E  F,  be  three  surfaces  placed  respectively 
at  the  distances,  1  ft.,  2  ft.,  and  3  ft.  from  a  lamp  at  L. 
The  same  amount  of  light  which  is  cast  upon  A  B  would 

*  Foucault  has  devised  an  ingenious  apparatus,  by  means  of 
which  he  has  determined  the  velocity  to  be  185,157  miles  per 
second — a  result  nearly  agreeing  with  that  of  Reamer,  if  we 
accept  the  more  generally  received  opinion  among  modern 
astronomers  in  regard  to  the  real  distance  of  the  earth  from  the 
sun, 


36 


LIGHT. 


be  cast  upon  C  D,  a  surface  four  times  as  great,  there- 
fore the  intensity  of  light  there  is  one-fourth  of  what  it  is 
at  A  B.  Again,  the  same  amount  of  light  which  is  cast 
upon  A  B  would  be  cast  upon  E  F,  a  surface  nine 


Fig.  21. 

times  as  great,  hence  tne  intensity  there  will  be  one- 
iiinth  of  what  it  is  at  A  B,  and  so  on;  the  distances 
being,  therefore,  expressed  by  the  numbers  1,  2,  3,  4,  5, 
etc.,  the  intensities  will  be  expressed  by  the  numbers 
1>  f»  ¥>  T&*  A>  e^c-  Such  is  the  numerical  expression  of 
the  law  of  inverse  squares. 

33.  Measurement  of  Light  —  Photometers.  —  By 
means  of  the  law  just  explained,  we  can  very  easily  com- 
pare one  kind  of  light  with  another,  and  express  numeri- 
cally their  relative  illuminating  powers.  One  of  the 


Fig.  22. 

simplest  methods  is  what  is  known  as  the  "shadow  test." 
It  consists  in  making  the  two  lights,  A  and  B  (fig.  22), 
cast  shadows  of  a  rod  C  upon  a  screen,  and  adjust- 
ing the  lights  till  the  shadows  at  E  and  F  are  illumin- 
ated to  an  equal  degree.  Now,  since  the  shadow  E  is 


LIGHT  IN  ITSELF  INVISIBLE.  37 

illuminated  by  the  light  B,  and  the  shadow  F  by  the 
light  A,  and  these  shadows  are  equally  bright,  it  follows 
that  the  lights  A  and  B  cast  the  same  quantities  of  light 
on  the  screen  at  their  respective  distances.  From  the 
previous  law  it  is  easily  inferred  that  the  intensities  are 
in  direct  proportion  to  the  squares  of  these  distances. 
Hence,  if  B  be  2  feet  from  the  screen,  and  A  5  ft.,  the 
relative  intensities  will  be  as  4  to  25,  or  A  gives  6  J  times 
as  much  light  as  B. 

The  art  of  thus  comparing  or  measuring  one  light  with 
another  is  called  Photometry.  Several  instruments  have 
been  constructed  with  the  view  of  carrying  out  the  same 
object;  these  are  termed  Photometers. 


CHAPTEK  II. 

34.  Beflection  of  Light — Irregular  or  Scattered. — 
Objects  are  rendered  visible  to  us  in  consequence  of  their 
powers  to  reflect  or  scatter  the  light  which  falls  upon 
them  in  all  directions.     If  an  object  did  not  possess  this 
power,  it  would  be  invisible.     It  is  owing  to  irregular 
reflection  from  the  particles  of  the  air  and  the  vesicles  of 
moisture  in  our  atmosphere  that  we  have  the  sun's  light 
so  universally  diffused,  and  gladdening  so  unsparingly  the 
entire  animal  and  vegetable  creation. 

35.  Light    in   Itself   Invisible. — A  beam  of   light 
entering  by  a  shutter  in  a  darkened  room  is  rendered 
visible  by  its  illuminating  the  particles  of  dust  in  its 
track.     Were  there  no  dust  particles  the  beam  would  be 
invisible.     A  striking  proof  of  this  is  afforded  by  placing 
the  end  of  a  poker  made  white-hot  at  some  point  in  the 
course  of  the  beam,  the  dust  particles  are  burnt  up,  and 
the  end  of  the  poker  is  shrouded  in  darkness.     If  several 
white-hot  bodies  be  so  placed,  the  beam  is  seen  broken 
up  into  several  parts. 


38  LIGHT. 

30.  Regular  Reflection— Plain  Mirrors.— If  light 
fall  upon  a  polished  surface,  such  as  a  plain  mirror,  it 

is  regularly  reflected, 
that  is,  it  is  sent  off 
the  reflector  in  a  de- 
finite direction.  Thus, 
let  A  B  be  a  plain 
mirror  (fig.  23).  If  the 
ray  of  light  fall  perpen- 
dicularly upon  it,  as  in 
the  direction  F  D,  it 
is  reflected  directly 
back  again.  But  if 
it  come  in  the  direc- 
tion C  D,  then  it  is 
reflected  in  the  direction  D  E,  the  angle  CDF  being 
equal  to  the  angle  F  D  E.  The  angle  C  D  F  is  called 
the  angle  of  incidence,  and  the  angle  F  D  E  the  angle  of 
reflection.  Moreover,  the  incident  ray  C  D  and  the  re- 
flected one  D  E  are  in  the  same  plane,  which  is  per- 
pendicular to  the  reflecting  surface.  The  law  of  regular 
reflection,  therefore,  may  be  expressed  thus :  the  angle 
of  incidence  is  always  equal  to  the  angle  of  reflection,  the 
incident  and  the  reflected  rays  being  in  the  same  plane, 
which  is  perpendicular  to  the  reflecting  surface. 

It  may  be  proved  by  geometry  that  the  course  C  D  E 
is  the  shortest  possible  from  the  points  C,  E,  to  the  mirror. 
It  is  shorter,  for  example,  than  the  course  C  G  E. 

37.  Influence  of  Obliquity. — The  number  of    rays 
which  are  reflected  from  a  regularly  reflecting  surface 
depends  upon  the  magnitude  of  the  angle  of  incidence. 
Thus,  in  the  case  of  water,  it  has  been  found  that  out  of 
1000  rays,  when  the  angle  is  40°,  22  rays  are  reflected; 
60°,  65  rays;  80°,  333  rays;  and  89 J°,  721  rays. 

38.  Formation  of  Images  by  Plain  Mirrors. — When 
an  object  is  placed  before  a  plain  mirror,  its  image  is 
seen  as  far  behind  the  mirror  as  the  object  itself  is  before 
'it.     This  is  a  consequence  of  the  foregoing  law. 


LATERAL  INVERSION. 


39 


Firstly,  let  us  take  the  case  merely  of  a  point  A  (fig.  24); 
tlie  rays  from  it,  after 
reflection  by  the  mir- 
ror, enter  the  eye  of 
a  spectator  at  E  in 
a  state  of  divergence — 
the  eye  receives  these 
rays  as  if  they  came 
from  the  point  A'  be- 
hind the  mirror.  By 
geometry  it  is  easily 
proved  that  the  dis- 
tance A  '  0  =  A  0  ; 
hence  the  truth  of  ^  0^ 

the  proposition. 

Secondly,  let  A  B  be  the  object  (fig.  25),  the  rays  from 
A,  after  reflection  by  the  mirror,  enter  the  eye  as  if  they 
came  from  a  real  object  at  A';  similarly,  the  rays  from  B 
enter  the  eye  as  if  they  came  from  B',  and  intermediate 
points  in  A  B  are  seen  at 
intermediate  points  in  A'B'. 
Thus,  an  image  of  AB  is 
seen  at  A'  B'.  The  image 
thus  formed  is  called  a  vir- 
tual image. 

39.  Lateral  Inversion. — 
The  image  formed  by  a  plain 
mirror  has  the  same  size  and 
shape  as  the  object,  but  dif- 
fers in  regard  to  position. 
If,  for  example,  a  person 
stands  before  a  looking- 
glass,  his  right  eye  is  the 
left  in  the  image,  and  his  Fig.  25 

left  eye  the  right  in  the  image.  This  effect  is  known  as 
lateral  inversion.  Hence,  writing  written  backward  is 
adjusted  by  being  held  before  a  mirror,  and  can  be 
read  as  if  it  were  written  in  the  ordinary  way.  A  set 


40 


LIGHT. 


of  types  arranged  for  printing  can  be  read  off  in  like 
manner.  The  blocks  made  for  wood-cut  illustrations 
may  be  examined  in  this  way  before  they  are  actually 
used. 

40.  Simple  Experiments  —  Curious  Facts  —  Some 
interesting  experiments  may  be  performed  with  a  com- 
mon looking-glass.  If  a  candle  be  held  directly  between 
the  eye  and  the  mirror,  one  image  only  of  the  candle  is 
seen.  Now,  if  the  candle  be  moved  gradually  towards 
the  side  of  the  mirror,  a  series  of  images  more  and  more 
detached  from  each  other  are  observed,  the  second  of  the 
series  being  the  brightest  and  best  denned.  The  experi- 
ment is  more  successful  in  a  darkened  room,  and  with  a 
mirror  having  a  thick  glass. 

"The  first  image  of  the  series  arises  from  the  reflection 
of  the  light  from  the  anterior  surface  of  the  glass.  The 
second  image,  which  is  usually  much  the  brightest,  arises 
from  the  reflection  at  the  silvered  surface  of  the  glass. 
.  .  .  ,  The  other  images  of  the  series  are  produced 
by  the  reverberation  of  the  light  from  surface  to  surface 
of  the  glass.  At  every  return  from  the  silvered  surface 
a  portion  of  the  light  quits  the  glass  and  reaches  the  eye, 
forming  an  image;  a  portion  is  also  sent  back  to  the 
silvered  surface,  when  it  is  again  reflected.  Part  of  this 
reflected  beam  also  reaches  the  eye  and  yields  another 
image.  This  process  continues;  the  quantity  of  light 
reaching  the  eye  growing  gradually  less,  and  as  a  conse- 
quence the  successive  images  growing  dimmer,  until 
finally  they  become  too  dim  to  be  visible."  * 

If  the  angle  of  incidence  be  made  large  by  holding 
the  candle  very  close  to  the  mirror,  whilst  the  eye  is 
placed  in  a  corresponding  position,  the  first  image  may 
be  made  to  appear  as  bright  or  even  brighter  than  the 
second  image,  affording  a  striking  proof  of  the  influence 
of  obliquity. 

If,  when  a  mirror  is  set  at  an  angle  of  45°,  an  object 
be  placed  vertically  before  it,  its  image  appears  in  a 
*  Tyndall's  Notes  on  Light,  p.  10. 


POLEMOSCOPE. 


41 


horizontal  position,  and  if  horizontally  its  image  appears 
vertical.' 

If  a  mirror  be  moved  parallel  to  itself,  either  from,  or 
towards  an  object,  the  image  moves  twice  as  fast;  or,  if 
it  be  made  to  rotate,  the  angle  through  which  the  image 
moves  is  twice  the  angle  through  which  the  mirror 
moves.  These  facts  all  follow  from  the  law  of  reflection, 
and  are  not  difficult  of  proof. 

If  an  individual,  standing  before  a  large  mirror,  see 
his  whole  person,  there  is  only  half  the  length  of  the 
mirror  concerned  in  the  production  of  the  image.  The 
reason  of  this  will. appear  from  fig.  26.  By  geometry 


Fig.  2G. 

the  triangles  A  C  D,  A  E  F,  are  similar,  therefore  A  C 
bears  the  same  proportion  to  A  E  as  C  D  does  to  E  F, 
but  A  C  =  \  A  E  (Art.  38),  therefore  C  D  =  £  E  F. 

41.  Polemoscope. — Light,  like  sound,  is  capable  of  re- 
peated reflection.  In  the  polemoscope  (fig.  27),  an 
instrument  of  some  service  in  the  time  of  war,  two  mir- 
rors are  used.  They  are  adjusted  at  an  angle  of  45°  to 
the  horizon.  The  upper  mirror  being  directed  towards  a 
distant  object,  the  rays  of  light  from  the  object  are  re- 
flected by  it  and  sent  down  upon  the  lower  mirror,  when 
they  are  again  reflected,  and  where  an  image  of  the  object 
is  seen. 

The  officers  behind  a  fortification  or  parapet  can,  with 


LIGHT. 


this  instrument,  watch  the  movements  of  the  enemy  with- 
out exposing  themselves  to  danger,  and  can  thus  give 
orders  to  their  men  how  to  direct  their  fire  to  the  best 
advantage. 


Fig.  27 

42.  Multiplication  of  Images — The  Kaleidoscope. — 
When  two  plane  mirrors  are  set  at  right  angles  to  each 
other,  an  object  placed  between  them  yields  three  images. 
Thus,  let  BC,  C  D  (fig.  28),  be  the  mirrors,  and  A  the 
object.  An  image  of  A  is  formed  in  the  mirror 
B  C  at  A',  a  second  in  the  mirror  C  D  at  A",  whilst  a 
third  image  is  formed  by  a  double  reflection  of  the  rays 


THE   KALEIDOSCOPE.  43 

at  A'".  The  three  images  and  the  object  are  in  the 
angles  of  a  rectangle.  If  A  be  at  equal  distances  from 
the  mirrors,  they  are  in  the  angles  of  a  square.  The 
number  of  images  in- 
creases as  the  angle 
betAveen  the  mirrors 
diminishes.  If  the 
angle  be  60°,  there  are 
5  images  ;  45°,  7  ;  30°, 
11.  In  general,  to  find 
the  number  we  have 
only  to  divide  360°  by 
the  angle  between  the 
mirrors,  and  diminish 
the  quotient  (if  a 
whole  number)  by 
unity.  Hence,  if  the 
angle  be  0°,  that  is,  if 
the  mirrors  be  par-  Fig.  23. 

allel,  the  number  of  images  is  infinite,  but  practically 
the  images  become  in  the  end  so  feeble  as  to  cease  to  be 
visible.  That  there  is  theoretically  an  infinite  number 
of  images,  may  be  seen  from,  the  following  reasoning  : 
Let  A  and  B  be  the  two  mirrors,  and  C  an  object  placed 
between  them.  An  image  of  C  is  formed  at  C'  by  the 
mirror  A,  as  far  behind  as  the  object  is  before ;  but  C' 
serves  as  an  object  for  the  mirror  B,  an  image  of  it, 
therefore,-  is  formed  at  C",  as  far  behind  B  as  C'  is  before 
it.  Similarly  an  image  of  C"  is  formed  at  C'"  by  the 
mirror  A,  and  so  on  ad  infinitum. 

An  arrangement  of  this  kind  is  sometimes  called  the 
"  endless  gallery,"  and  is  used  in  ball-rooms,  picture 
galleries,  jewellers'  shops,  etc.,  in  order  to  add  to  their 
appearance  and  produce  a  dazzling  effect. 

The  kaleidoscope  (invented  by  Brewster)  depends  for 
its  effect  upon  the  multiplication  and  symmetrical  arrange- 
ment of  images.  It  consists  of  a  tube  of  metal  or  card- 
board, in  which  are  placed  two  strips  of  silvered  glass  set 


44:  LIGHT. 

at  an  angle ;  at  the  end  are  the  Small  objects,  such  as 
pieces  of  coloured  glass,  beads,  straws,  etc.,  confined  be- 
tween two  glass  discs.  Looking  through  the  narrow 
aperture  at  the  other  end,  and  turning  round  the  instru- 
ment, an  infinite  variety  of  arrangement  is  effected  in  the 
small  objects,  and  therefore  also  an  infinite  number  of 
beautiful  forms  is  presented  to  the  eye. 

43.  Reflection  from  Curved  Mirrors.— The  most 
common  forms  of  curved  reflectors  are  the  concave 
spherical  and  the  convex  spherical. 

The  first  of  these  is  the  more  important  to  notice.  Let 
AB  be  the  mirror  (fig.  29),  0  the  centre  of  the  spherical 


Fig.29. 

shell,  of  which  the  mirror  forms  a  portion,  C  D  a  lino 
drawn  through  O  and  the  middle  point  of  the  mirror. 
This  line  is  termed  the  principal  axis.  Rays  passing 
from  the  point  O  are  reflected  directly  back.  If  the  rays 
come  from  an  infinite  distance,  or  from  the  sun,  they  may 
be  considered  as  coming  in  parallel  directions,  and 
after  reflection  by  the  mirror,  they  are  concentrated 
in  the  point  F,  midway  between  O  and  D.  This 
point  is  called  the  principal  focus.  But  if  they  come 
from  a  point  C,  the  divergent  beam  is  concentrated  at 
some  point  C'  such  that  the  angle  C  A  O  is  equal  to 
the  angle  C'  A  0,  and  an  image  of  C  is  thus  formed  at 
C'.  Let  now  the  point  C  approach  the  mirror,  the  focus 


REFLECTION  FRO^I  CURVED  MIRRORS.  45 

C'  will  move  towards  0.  Passing  0,  the  focus  of  the 
rays  moves  along  0  C,  until  the  point  conies  to  C',  when 
C  now  becomes  the  position  of  the  image.  The  two 


Fig.  30. 

points  C,  C',  are  tlius  interchangeable — they  are  called 
conjugate  points  or  foci.  When  the  luminous  point 
coincides  with  F,  the  rays  after  reflection  pass  in  par- 
allel directions.  If  the  point  still  approach  the  mirror, 
the  rays  become  divergent,  and  form  no  real  focus,  but 
if  produced  backwards,  as  in  fig.  30,  they  meet  in  some 
point  C',  that  is,  an  eye  placed  at  E  will  receive  the  rays 
as  if  they  came  from  C'.  In  such  a  case  C'  is  called  a 
virtual  focus. 

If  the  luminous  point  be  not  placed  on  the  principal 
axis,  the  position  of  its  image  is  determined  as  in 
fig.  31.  Draw  C  D  through  the  point  O — this  is  termed 
a  secondary  axis.  The  rays  are  brought  to  a  focus  upon 
this  axis  at  some  point  C',  between  the  principal  focus 
and  the  centre  of  curvature,  as  before. 

The  formation  of  the  image  of  an  object  by  this  kind  of 
mirror  will  now  be  easily  understood.  Let  A  B  be  the 
object  (fig.  32);  the  rays  from  A  will  be  brought  to  a 
focus  at  A',  and  the  rays  from  B  at  B'.  Thus  there  will 
be  formed  between  F  and  O  an  image  A'  B',  smaller 
than  the  object,  and  inverted.  Similarly,  if  A'  B'  be  the 


46  LIGHT. 

object,   A  B  will  be  its  image.     Both  these  images  are 

formed  in  the  air  in  front  of  the  mirror,  and  are,  there- 
fore, real  images. 


Fig.  31. 

If  the  object  be  placed  between  the  principal  focus 
and  the  mirror  (fig.  33),  then  the   rays  from  the  object 


Fig.  32. 

A  B  enter  the  eye  at  E,  as  if  they  came  from  an 
object  behind  the  mirror  at  A'  B'.  In  this  case  the 
image  has  the  same  position  as  the  object,  and  is  mag- 
nified. It  is  a  virtual  image. 


SPHERICAL  ABERRATION — CAUSTICS.  47 

In  regard  to  the  convex  spherical  mirror  (fig.  34),  let 
A  B  be  the  object,  O  the  centre  of  curvature,  and  F  the 
principal  focus  (evidently  virtual).  The  rays  from  the 


Fig.  33. 

object  A  B,  after  reflection  by  the  mirror,  proceed  as  if 
they  came  from  an  object  at  A'  B'.  Thus  a  virtual 
image  is  seen  there  smaller  than  the  object,  and  in  the 
same  position. 


Fte.  34. 


44.  Spherical  Aberration — Caustics. — All  the  rays 


48 


LIGHT. 


from  a  luminous  point  which  fall  upon  a  concave  spheri- 
cal reflector,  are  not  concentrated  into  a  single  point, 
as  we  have  been  supposing.  The  rays  which  fall  upon 
the  marginal  parts  of  the  mirror  are  not  thus  concen- 
trated— these,  by  their  intersection  with  each  other,  give 
rise  to  a  series  of  images  forming  a  luminous  surface, 
which  is  called  a  caustic.  The  inability  of  a  concave 
mirror  to  collect  the  rays  falling  upon  it  into  one  point 
is  called  spherical  aberration. 

It  may  be  so  far  obviated  by  interposing  an  opaque 
diaphragm  in  such  a  way  as  to  restrict  the  rays  to  a 
small  portion  of  the  mirror  round  the  principal  axis. 
The  caustic  curve  may  be  well  seen  by  placing  a  common 
glass  tumbler  nearly  tilled  with  milk  beside  a  candle;  the 
rays  are  thrown  down  by  the  interior  face  of  the  glass, 
and  exhibit  the  curve  upon  the  lacteal  surface. 


CHAPTER  III. 


45.  Refraction  of  Light. — A  ray  of  light,  in  passing 
from  one  medium  into  an- 
other, is  said  to  be  refracted 
when  it  deviates  from  the 
direction  in  which  it  was 
proceeding  before  entering  the 
new  medium.  The  deviation 
itself  is  called  refraction.  Thus, 
take  the  media  air  and  water. 
Let  A  O  be  a  ray  passing  from 
air  into  water  (fig.  35).  If  it 
enter  the  water  in  the  perpen- 
dicular direction  AO,  it  goes 
straight  through  without  suf-  ^ 
fering  any  deviation;  but  if  it  & 
enter  in  the  direction  A'O,  in  Fig.  35. 

stead  of  pursuing  the  straight  course  0  C,  it  is  bent 


Y, 


LAW  OP  REFRACTION. 


49 


from  it,  and  takes  a  new  direction  OD.  The  angle  A'O  A 
is  termed  the  angle  of  incidence)  and  DOB  is  termed  the 
angle  of  refraction. 

It  will  be  seen,  therefore,  that  the  behaviour  of  the 
ray  is  this:  when  it  passes  from  air  into  water  it  is 
refracted  towards  the  perpendicular,  and,  conversely, 
when  it  passes  from  water  into  air  it  is  refracted  from 
the  perpendicular. 

46.  Law  of  Refraction. — But  the  refraction  of  light 
obeys  a  more  definite  principle  than  that  just  mentioned. 
To  understand  what  that  is,  suppose  we  describe  a  circle 
with  any  radius  0  A  (fig.  36),  and  draw  A'  F,  D  G,  per- 


Fig.  36. 

pendicular  to  AB,  then  it  is  found  whatever  be  the 
magnitude  of  the  angle  A'  0  A,  that  the  relation  between 
A'F  and  DG  is  always  the  same,  or,  as  it  is  often 
expressed,  the  ratio  ^-|.  *  is  a  constant  quantity. 
This  constant  quantity  is  called  the  index  of  refraction. 
For  air  and  water  the  index  is  -J-,  and  for  air  and  glass  -|. 
If  the  course  of  the  ray  be  reversed,  the  indices  are 

*  If  the  radius  of  the  circle  be  1,  A'  F  is  the  sine  of  the  angle 
of  incidence,  and  D  G  the  sine  of  the  angle  of  refraction ;  hence, 
the  law  may  be  expressed  thus:  "the  sine  of  the  angle  of  inci- 
dence bears  to  the  sine  of  the  angle  of  refraction  a  constant  ratio," 


50  LIGHT. 

respectively  f  and  f .  In  general,  the  greater  the  refrac- 
tive index  between  two  media,  the  greater  the  deviation 
of  the  ray  from  its  original  path. 

47.  Effects  of  Refraction. — The  refraction  of  light 
explains  a  number  of  familiar  phenomena.  A  pool  of 
water  appears  shallower  than  it  really  is.  To  under- 
stand this,  let  A  (fig.  37)  be  a  point  in  the  bottom,  the 
rays  A  B,  A  C,  in  emerging  from  the  water  are  refracted 
in  the  directions  B  E,  C  E,  and  enter  the  eye  there  as  if 
they  came  from  the  point  A'  near  the  perpendicular, 
that  is,  the  point  A  will  be  seen  at  A'.  The  same  is 
true  of  every  other  point,  hence  the  whole  bottom  of  the 
pool  appears  lifted  up.  From  this  it  is  manifest  that 


Fig.  37.  Fig.  S3. 

the  more  divergent  the  rays  B  E,  C  E  are,  in  other 
words,  the  greater  the  obliquity  of  the  vision,  the  shal- 
lower will  the  pool  appear. 

A  stick  placed  vertically  in  water  (fig.  38)  appears 
shortened,  and  placed  obliquely  appears  bent,  the  im- 
mersed portion  being  raised  by  refraction. 

An  object  under  water  appears  not  only  less  deep,  but 
also  of  a  different  shape  (fig.  39).  Thus  the  object  A  B 
will  appear  to  have  the  position  and  shape  A'  B'. 

A  boat  floating  in  clear  water  seems  to  have  a  flatter 
bottom  than  it  really  has,  so  also  a  deep-bodied  fish 
seems  contracted. 


REFRACTION  ACCOMPANIED  BY  REFLECTION.  51 

A  striking  effect  of  refraction  is  exhibited  by  the 
following  experiment : — Place  a  coin  in  a  bowl,  and  re- 

tire  until  you  just  lose 
sight  of  the  coin  by  the 
interposition  of  the  edge. 

Now  desire  a  companion 

to  fill  the  bowl  with  water, 
the  coin  again  comes  into 
-\-^:/  -'i    view. 

\,?  In  consequence    of   re- 

"   fraction     by     the     atmo- 
sphere, we  never  see  the 

heavenly  bodies  in  their  true  places,  except  those 
which  are  directly  over  our  heads.  The  amount  of 
displacement  near  the  horizon  is  estimated  at  about 
half  a  degree,  but  it  diminishes  rapidly  towards  the 
zenith.  When  we  see  the  lower  edge  or  limb  of  the 
sun  or  moon  apparently  just  touching  the  horizon,  the 
whole  disc  is  actually  below  it.  Hence  refraction  tends 
to  prolong  the  stay  of  the  sun  and  moon  above  the 
horizon — it  hastens  their  rising,  and  delays  their  setting. 
Even  after  the  sun  has  disappeared  below  the  horizon, 
the  refraction  of  his  rays  continues  for  some  time,  which, 
combined  with  reflection,  produce  the  phenomenon  of 
twilight,  by  which  we  pass,  with  so  pleasing  a  gradation, 
"from  the  effulgence  and  activity  of  day  to  the  darkness 
and  stillness  of  night. 

48.  Refraction  is  always  Accompanied  by  Reflection. 
— Wherever  there  is  refraction,  there  is  also  reflection. 
We  cannot  have  the  one  without  the  other.  Should  the 
one  disappear,  so  will  the  other.  The  higher  the  refrac- 
tive power  of  a  substance,  the  greater  the  amount  of 
reflection;  hence  the  striking  brilliancy  of  the  dia- 
mond. 

It  will  not  be  difficult,  therefore,  to  understand  the 
appearance  presented  on  the  margin  of  a  river  or  lake. 
Thus,  in  fig.  4-0  the  rays  from  the  objects  on  the  opposite 
bank  partly  enter  the  water,  suffering  refraction,  and 


52 


LIGHT. 


are  partly  reflected  from  the  surface  towards  the  observer. 
In  virtue  of  this   partial  reflection,  inverted  images  of 


Fig.  40. 

the  objects  are  seen,  and  they  axe  feeble,  because  of  tho 
loss  of  the  light  which  passes  into  the  water. 

49.  Transparency — Opacity  of  Transparent  Mix- 
tures.— There  is  no  body  perfectly  transparent,  that  is, 
none  which  allows  perfect  freedom  in  the  transmission 
of  light.  Water,  for  instance,  is  transparent  at  ordinary 
depths,  but  even  then  a  number  of  rays  are  quenched. 
At  the  depth  of  a  few  hundred  feet  it  would  lose  all  its 
transparency.  The  dimness  of  the  sun  and  moon  in  the 
horizon  is  owing  to  some  of  the  light  being  quenched  in 
its  passage  through  the  atmosphere.  "Were  our  atmo- 
sphere 700  miles  high,  we  should  have  no  sunlight. 

"In  the  passage  from  one  medium  to  another  of  a 
different  refractive  index,  light  is  always  reflected;  and 
this  reflection  may  be  so  often  repeated  as  to  render  the 
mixture  of  two  transparent  substances  practically  im- 
pervious to  light.  It  is  the  frequency  of  the  reflec- 
tions at  the  limiting  surfaces  of  air  and  water  that 
renders  foam  opaque.  The  blackest  clouds  owe  their 
gloom  to  this  repeated  reflection,  which  diminishes  their 
transmitted  light,  hence  also  their  whiteness  by  reflected 
light.  To  a  similar  cause  is  due  the  whiteness  and  im- 
perviousness  of  common  salt,  and  of  transparent  bodies 


TOTAL  KEFLECTION. 


53 


generally  when  crushed  to  powder.  The  individual 
particles  transmit  light  freely;  but  the  reflections  at 
their  surfaces  are  so  numerous  that  the  light  is  wasted 
in  echoes  before  it  can  reach  to  any  depth  in  the  powder. 
The  whiteness  and  opacity  of  writing  paper  are  due 
mainly  to  the  same  cause.  It  is  a  web  of  transparent 
fibres,  not  in  optical  contact,  which  intercept  the  light 
by  repeatedly  reflecting  it.  But  if  the  interstices  of  the 
fibres  be  filled  by  a  body  of  the  same  refractive  index  as 
the  fibres  themselves,  the  reflection  of  the  limiting  sur- 
faces is  destroyed,  and  the  paper  is  rendered  transparent. 
This  is  the  philosophy  of  the  tracing-paper  used  by 
engineers.  It  is  saturated  with  some  kind  of  oil,  the 
lines  of  maps  and  drawings  being  easily  copied  through 
it  afterwards.  Water  augments  the  transparency  of  paper, 
as  it  darkens  a  white  towel;  but  its  refractive  index  is  too 
low  to  confer  on  either  any  high  degree  of  transparency."  * 
50.  Total  Reflection  —  The  Limiting  Angle.  —  In 
order  that  a  ray  of  light  may  pass  from  a  dense  medium 
into  a  rarer,  the  angle  of  incidence  must  not  exceed  a 
certain  limit.  For  water  and  air  this  angle  is  about 
48J°,  and  is  called  the  limiting  or  critical  angle  of  re- 
fraction. Thus,  let  A  B  be  the  incident  ray  (fig,  41), 
then  if  the  angle 
ABC-  48-|-°,  the 
refracted  ray  will 
emerge  in  the  direc- 
tion B  E,  or  parallel 
to  the  surface  of  the 
water.  If  the  angle 
A  B  C  be  greater  than 
48J-°,  then  the  ray  is 
ivholly  reflected,  that 
reflection  obeying  the 
ordinary  law.  It  fol- 
lows from  this,  that  Fig.  41. 
all  the  incident  light  embraced  in  the  angular  space 
*  Tyndall's  Notes  on  Light,  p.  19. 


54 


LIGHT. 


D  B  E,  is  condensed  by  refraction  into  the  space  ABC, 
or  that  the  whole  light  which  passes  into  the  water  is 
condensed  into  an  angular  space  of  97°. 

"We  can  imagine,  therefore,  what  kind  of  appearance  is 
presented  to  a  diver,  in  still  shallow  water;  when  he  looks 
upwards,  all  external  objects  will  be  seen,  as  it  were, 
through  a  circular  aperture  overhead  of  97°  in  diameter, 
whilst  beyond  this  circle  he  will  see,  by  the  effect  of  total 
reflection,  the  various  objects  at  the  bottom  as  distinctly 
as  if  he  looked  directly  at  them.  A  man  standing  on  the 
shore,  as  well  as  the  shore  itself,  would  appear  to  be  lifted 
up. 

Total  reflection  may  bo  well  illustrated  by  placing  a 
coin  in  a  tumbler  of  water,  and  sloping  the  tumbler 
till  the  light  acquires  the  proper  incidence.  On  looking 
upwards  a  distinct  image  of  the  coin  is  seen  towards  the 
surface  of  the  water.  In  an  aquarium,  if  the  eye  be 
directed  to  the  surface  of  the  water,  the  various  objects 
in  it  may  be  rendered  visible  in  a  like  manner. 

51.  Lenses — Converging  and  Diverging. — A  lens  is 
a  portion  of  a  refracting  substance,  such  as  glass,,  having 
its  bounding  surfaces  either  both  curved,  or  the  one  plane 
and  the  other  curved.  Lenses  are  of  two  classes,  con- 
verging and  diverging,  and  are  named  from  the  form  of 
their  external  surfaces.  Each  class  comprises  three  kinds. 


Converging.       Fig.  42.        Diverging. 

Thus  (fig.  42),  A  is  called  a  double  convex  lens;  B,  a 
plano-convex;  C,  a  concavo-convex  (or  meniscus),  the 
convex  surface  having  the  greater  curvature.  D  is  called 
a  double  concave  lens;  E,  a  plano-concave,  and  F,  a  con- 
vexo-concave,  the  concave  surface  having  the  greater  cur- 
vature. 


DOUBLE   CONVEX   LENS. 


55 


The  effect  of  a  converging  lens  as  A,  and  of  a  diverging 
lens  as  B,  on  a  beam  of  light,  will  be  understood  from 
figs.  43,  44. 

Let  the  beam  con- 
sist of  parallel  rays; 
the  lens  A  (fig.  43) 
brings  the  rays  to  a 
focus  at  the  point  F. 
This  point  is  called 
the  principal  focus, 
that  is,  it  is  the  fo- 
cus of  parallel  rays. 
It  is  a  real  focus. 

Again,  the  lens  B 
(fig.  44)  causes  the 
rays  to  diverge,  as  if 
they  came  from  a 
point  F',  on  the  same 
side  of  the  lens  on. 
which  the  light  falls. 
This  point  is  there- 
fore the  principal  fo- 
cus. It  is  evidently 
a  virtual  focus. 

It  may  be  noticed  that  a  converging  lens  is  thicker  and 
a  diverging  lens  thinner  at  the  centre  than  at  the  exterior 
borders.  They  may  therefore  be  distinguished  very 
easily  in  this  way. 

52.  Formation  of  an  Image  by  a  Double  Convex 
Lens. — Let  us  first  take  the  case  of  a  luminous  point 
placed  before  a  double  convex  lens.  Let  A  be  the 
luminous  point  (fig.  45) ;  draw  A  A'  through  the  centre 
of  the  lens,  perpendicular  to  its  two  convex  surfaces — 
this  is  termed  the  principal  axis.  The  rays  from  A 
are  brought  to  a  focus  at  a  point  A'  beyond  the  prin- 
cipal focus  F,  and  a  real  image  of  A  is  formed  there. 
These  two  points,  as  before,  are  convertible;  they  are 
conjugate  foci.  If  A  now  be  moved  towards  the  lens, 


Fig.  44 


56  LIGHT. 

A'  will  retire  from  it,  until  A  coincides  with  the  prin- 
cipal focus  F'  (O  F  being  equal  to  O  F'),  when  the  rays, 
as  in  fig.  43,  will  emerge  from  the  lens  in  paralled  direc- 
tions. 


Fig.  45. 

If  A  be  placed  between  F'  and  the  lens  (fig.  4G),  the 
rays,  after  passing  through  the  lens,  are  divergent,  pro- 
ceeding as  if  they  came  from  a  point  A'.  The  point  A' 
is  therefore  a  virtual  focus. 


Fig.  4G. 

Let  now  an  object  A  B  be  placed  before  the  lens 
beyond  the  principal  focus  (fig.  47).  Draw  A  O  A'  and 
BOB'  through  the  centre  of  the  lens.  The  rays  from  A 
are  brought  to  a  focus  at  A',  those  from  B  at  B',  and  the 
rays  from  intermediate  points  in  A  B  at  intermediate 
points  in  A'  B'.  Thus  a  real  inverted  image  of  A  B  will 
be  formed  at  A'  B'.  This  image  may  be  seen  by  an  eye 
placed  beyond  A'  B',  or  it  may  be  projected  on  a 
screen,  whose  distance  from  the  lens  is  equal  to  that  of 
A'  B'.  The  size  of  the  image  bears  the  same  proportion 


DOUBLE    CONCAVE  LENS. 


57 


to  the  size   of    the   object,  as   the  distance    0  A'  does 
to  OA. 


Fig.  47. 

If   the   object   be   placed   between  the   lens   and   the 
principal  focus  (fig.  48),  a  magnified  and  erect  image  will 


Fig.  48 

be  formed.     Then,  of  course,  the  image  is  virtual, 
an  arrangement  constitutes  the  simple  microscope. 


Such 


Fig.  49. 

53.  Formation  of  an  Image  by  a  Double  Concave 
Lens. — We  have  seen  that  a  double  convex  lens  may  give 
either  a  real  or  a  virtual  image,  according  to  the  distance 


LIGHT. 

of  the  object.  A  double  concave  lens  gives  only  a  virtual 
image  at  all  distances.  Let  A  B  be  the  object  (fig.  48), 
F  C  the  principal  axis,  F  the  principal  focus.  The 
rays  from  A  B,  after  traversing  the  lens,  are  divergent, 
and  enter  the  eye  as  if  they  came  from  a  real  object  at 
A'  B',  that  is,  there  will  be  an  image  of  A  B  seen  at 
A'  B',  between  the  lens  and  the  principal  focus.  That 
image  is  erect  and  smaller  than  the  object. 

54.  Camera  Obscura. — This  instrument  is  represented 
scctionally  in  fig.  50.     It  consists  of  a  sloping,  wooden 


Fig.  50. 


box,  blackened  inside,  to  obviate  irregular  reflection,  at 
the  bottom  of  which  is  placed  a  sheet  of  paper.  At  the 
top  there  is  a  small  cubical  box,  formed  of  two  parts, 
one  of  which  slides  into  the  other,  for  the  purpose  of 
focal  adjustment,  and  which  contain  respectively  a  plane 
reflector  and  a  double  convex  lens.  The  action  of  the  in- 
strument is  this :  The  rays  from  some  distant  object, 
AB,  are  reflected  by  the  mirror  towards  the  lens;  the 
lens  concentrates  these  rays  into  a  focus,  and  an  image 
A'  B'  is  thus  formed  upon  the  paper.  There  are  two  aper- 
tures, through  one  of  which  the  picture  is  viewed,  and 


SPHEIUCAL   ABERRATION.  50 

through  the  other  the  hand  may  be  thrust  for  the  pur- 
pose of  sketching  it  off. 

55.  Magic  Lantern. — The  construction  and  principle 
of  this  instrument  will  be  understood  from  fig.  51.     The 


Fig.  51. 

lamp  L  is  placed  in  the  focus  of  a  concave  reflector  R ; 
the  rays  from  it,  after  reflection,  are  condensed  by  the 
lens  A  upon  the  glass  slide  C,  on  which  the  picture  is 
painted.  An  image  of  the  illuminated  picture  is  then 
formed  by  the  lens  B,  and  thrown  upon  the  screen  in  a 
darkened  room.  The  lens  B  is  fixed  in  a  tube  which 
slides  into  the  other,  and  its  focus  can  therefore  be  ad- 
justed to  different  distances.  From  what  we  have  seen 
in  regard  to  the  formation  of  an  image  by  a  lens,  the 
slide  C  must,  of  course,  be  introduced  in  an  inverted  posi- 
tion. The  image  on  the  screen  is  magnified  as  many 
times  as  the  distance  of  the  screen  from  B  contains  the 
distance  of  C  from  B. 

Dissolving  views  are  produced  by  having  two  similar 
magic  lanterns,  placed  side  by  side,  and  directed  towards 
the  same  part  of  the  screen.  A  metallic  diaphragm  is 
placed  before  the  lanterns,  and  is  so  arranged  as  gradually 
to  close  the  aperture  of  the  one  lantern,  whilst  that  of 
the  other  is  being  opened.  By  this  artifice  a  pleasing 
variety  of  effect  is  obtained. 

56.  Spherical  Aberration. — We  have  been  proceeding 
upon  the  supposition  that  all  the  light  passing  through 
a  lens  is  brought  to  the  same  focus.  This,  in  reality,  is 
not  the  case.  The  rays  which  fall  upon  the  exterior 
borders  of  the  lens  are  not  concentrated  into  the  same 


CO 


LIGHT. 


point,  but  are  found  to  intersect  each  other  at  different 
points,  forming  a  luminous  surface,  which  is  called  a  caustic, 
by  refraction  (Art.  44).  This  inability  on  the  part  of  a 
lens  to  bring  all  the  rays  to  a  single  focus,  is  called 
spherical  aberration. 

This  aberration  interferes  with  the  sharpness  or  dis- 
tinctness of  an  image,  but  may  be  partly  obviated  by 
interposing  an  opaque  diaphragm  provided  with  a  central 
aperture.  This  allows  the  rays  only  which  fall  upon 
the  central  part  of  the  lens,  to  pass  through.  Recourse 
is  had  to  this  device  in  photography. 


CHAPTER  IV. 

57.  The  Eye:  its  Structure.— The  different  parts  of 
this  wonderful  organ  are  exhibited  in  fig.  52. 


1,  is  called  the  cornea;  2 — the  sclerotic  coat,  or  white  of 
the  eye;  3 — the  choroid  coat,  covered  with  a  black  pigment 
to  prevent  internal  reflection;  4 — the  delicate  network 
of  the  retina,  which,  being  an  extension  of  the  optic 
nerve  (5),  conveys  the  impression  of  the  image  there  de- 
picted to  the  brain.  Behind  the  cornea  is  an  opening 
called  the  pupil  (6),  surrounded  by  the  membrane  of  the 
iris  (7),  which  is  differently  coloured  in  individuals, 
giving  rise  to  difference  of  colour  in  eyes.  The  iris  per- 


PUNCTUM   CCECUM — FORAMEN   CENTRALE.  61 

forms  the  important  function  of  regulating  the  quan- 
tity of  light  which  passes  into  the  interior  chamber  of 
the  eye,  by  its  involuntary  action  in.  enlarging  or  con- 
tracting the  diameter  of  the  pupil.  8,  is  the  crys- 
talline lens,  more  convex  behind  than  before,  and  con- 
sisting of  concentric  layers  of  tissue,  which  increase  in 
consistency  towards  the  centre.  The  space  between  the 
cornea  and  the  lens  is  filled  with  a  fluid  like  water,  called 
therefore  the  aqueous  humour ;  whilst  the  whole  of  the 
posterior  chamber  is  filled  with  another  fluid,  called  the 
vitreous  humour,  from  its  resemblance  to  melted  glass. 

58.  Distinct  Vision. — In  order  that  we  may  see  any 
external  object  distinctly,  an  image  of  that  object  must  be 
thrown  upon  the  retina;   in  other  words,  the  rays  of 
light  from  the  object  must  be  brought  to  a  focus  there, 
(fig.  52).     This  is  effected  chiefly  by  the  intervention  of 
the  cornea ;  but  the  other  parts  of  the  eye,  the  aqueous 
humour,  the  crystalline  lens,  and  the  vitreous  humour, 
are  all  concerned  in  the  refraction  of  the  rays. 

That  an  image  of  an  external  object  is  actually  depicted 
upon  the  retina,  has  been  shown  by  experimenting  with  the 
eye  of  a  recently  slaughtered  bullock.  What  holds  good 
of  a  bullock's  eye,  is  believed  to  be  true  of  the  human  eye. 
The  image  also  is  inverted,  the  reason  of  which  is  obvious. 
For  ordinary  eyes  there  is  a  certain  distance  at  which  an 
object  must  be  placed,  in  order  that  it  may  be  seen  with 
the  greatest  possible  distinctness.  This  distance  of  distinct 
vision,  as  it  is  termed,  in  the  case  of  small  objects,  such  as 
common  type,  varies  from  10  to  12  inches. 

59.  Punctum  Coecum  —  Foramen  Centrale. — It  is  a 
remarkable  fact,  and  one  which  can  scarcely  be  credited, 
that,  though  the  optic  nerve  is  the  medium  of  communi- 
cation with  the  brain,  when  the  image  of  an  object  falls 
upon    the    base   of    that   nerve  (fig.  52),  there    is  no 
impression  produced — it  is  quite  insensible  to  the  action 
of  light.     The  following  interesting  experiment  may  be 
made  in  corroboration  : — Put  three  spots  of  ink  on  a  sheet 
of  paper,  about  three  inches  apart,  Shut  cue  eye,  and  look 


62  LIGHT. 

steadily  with  the  other  at  any  of  the  spots.  If  now  the 
head  be  slowly  moved  towards  either  side,  up  or  down,  a 
position  will  be  obtained  where  one  of  the  three  spots 
entirely  disappears.  By  a  little  care  any  one  of  the  spots 
may  be  made  to  vanish.  This  is  owing  to  the  image  fall- 
ing upon  the  surface  in  question.  From  this  circumstance 
the  surface  has  been  called  the  punctum  caecum,  or  "  blind 
spot." 

Every  part  of  the  retina  is  not  equally  sensitive  to  the 
action  of  light.  There  is  a  small  portion  where  the 
organization  seems  to  be  more  delicate  than  any  other. 
This  part  is  called  the  foramen  centrale,  or  "  central  open- 
ing." *  If  the  image  of  an  object  fall  upon  this,  it  is  seen 
with  the  greatest  possible  distinctness. 

The  retina  of  another  person's  eye  may  be  examined, 
and  this  part  thus  rendered  visible  by  an  instrument 
called  the  ophthalmoscope. 

60.  Why  Objects  are  Seen  Erect. — Since  the  image  of 
any  external  object  depicted  upon  the  retina  is  inverted, 
a    natural     question    arises,  how    do    we    correct    this 
inversion  1       Some  have     supposed    that    we    actually 
do    see    everything    inverted,    but    that,    from     habit 
and  experience,  we  learn  to  assign  to  every  object  its 
true  position.      According   to  this  opinion,  infants  see 
objects  upside  down;   and  it  is  only  by  comparing  the 
erroneous  information  acquired  by  vision,  with  the  more 
accurate  information  acquired  by  touch,  that  they  learn 
to  see  objects  as  they  really  are.     Others  again  account 
for  it  by  supposing  that  we  really  judge  of  the  position 
of  an  object  from  the  direction  in  which  the  rays  of  light 
j)roceeding  from  it  enter  our  eyes. 

61.  Single  Vision. — As  there  is  an  image   of  the 
object  in  each  eye,  it  may  be  asked,  why  is  it  we  do  not 
see  double  when  we  use  both  eyes?     This  question  is  not 
difficult  to  answer.     When  we  fix  our  eyes  upon    an 

*  This  name  is  apt  to  lead  to  misconception.  There  is  really 
no  part  of  the  retina  where  there  i§  a.n  "  opening,"  except  at  the 
base  of  the  optic  nerve. 


ADJUSTMENT  OP  THE  EYE  FOR  DIFFERENT  DISTANCES.     C3 

object,  each  eye  arranges  itself  in  a  particular  manner. 
Thus,  let  B,  C  be  the  two  eyes  (fig.  53),  and  A  the  object. 
Draw  A  a,  A  a  through  the  centre  of  the  crystalline  lens, 


Fig.  53. 

and  at  right  angles  to  the  convex  surfaces.  These  lines 
are  called  the  optic  axes,  and  the  angle  between  them, 
ft  A  a,  the  optical  angle.  The  eyes  adjust  themselves  so 
that  the  optic  axes  intersect  each  other  at  the  object. 
In  consequence  of  this,  a  precisely  similar  image  of  the 
object  is  formed  in  each  eye,  and  therefore  a  precisely 
similar  impression  of  the  object  is  conveyed  to  the  mind. 
If  either  eye  be  prevented  from  thus  adjusting  itself  by 
slight  pressure  on  the  eye-ball,  double  vision  results. 
Hence  persons  who  squint  have  always  double  vision.  It 
thus  appears  that  single  vision  arises  from  the  circum- 
stance that  the  image  is  cast  upon  corresponding  parts  of 
the  retina  in  both  eyes. 

If,  whilst  the  eyes  are  directed  upon  a  small  object  at 
A  (fig.  53),  there  is  another  object  A'  placed  beyond, 
that  latter  object  will  be  seen  double.  This  results  from 
the  images  in  the  two  eyes  being  thrown,  upon  different 
parts  of  the  retina.  Thus,  the  image  in  B  is  formed  on 
the  left  of  the  optic  axis,  and  that  in  C  on  the  right.  If 
the  eyes  be  directed  upon  A7,  then  A  will  be  seen  double 
for  the  same  reason. 

62.  Adjustment  of  the  Eye  for  Different  Distances. 


G4  LIGHT. 

— Experience  teaches  us  that  objects  are  seen  with  suffi- 
cient distinctness,  though  their  distances  may  vary  con- 
siderably. It  follows,  therefore,  that  the  eye  must  have 
the  power  of  accommodating  itself  to  the  distance  at 
which  an  object  is  situated.  Several  opinions  have  been 
entertained  on  this  matter.  Some  physicists  attribute 
it  to  a  property  which  the  crystalline  lens  possesses  of 
changing  its  curvature,  so  as,  in  every  case,  to  make  the 
rays  converge  to  a  focus  upon  the  retina.  Others  sup- 
pose that  it  is  dependent  upon  the  contraction  and 
dilatation  of  the  pupil.  According  to  this  hypothesis, 
objects  at  some  distances  are  seen  by  virtue  of  the  rays 
which  fall  upon  the  exterior  borders  of  the  lens;  whilst 
again,  near  objects  are  seen  by  virtue  of  the  rays  which 
pass  through  the  middle  of  the  lens,  such  rays  under- 
going thereby  a  greater  degree  of  refraction  than  in  the 
other  case.  Others,  again,  imagine  that  the  focal  dis- 
tance of  the  lens,  for  different  distances,  may  vary  so  little 
as  not  to  cause  any  appreciable  effect  on  the  distinctness 
of  the  image. 

63.  Long  and  Short  Sight — Spectacles. — In  advanced 
life  the  eye  loses  its  power,  and  becomes  incompetent  to 
bring  the  rays  to  a  focus  upon  the  retina  at  the  ordinary 
distance  of  distinct  vision.  This  condition  of  the  eye, 
which  is  common  to  most  elderly  persons,  is  termed  "far- 
sightedness." 


I 


Fig.  54. 

Let  E  be  such  an  eye,  and  AB  the  object  (fig.  54); 
the  rays  from  it  tend  to  converge   to   a  focus 


LONG   AXD   SHORT   SIGHT — SPECTACLES.  65 

the  retina,  and  an  image  of  the  object  would  be  formed 
at  A'  B';  the  rays,  therefore,  which  really  fall  upon  the 
retina,  are  in  a  state  of  separation,  each  produces  a  picture 
of  its  own,  and  indistinct  vision  is  the  consequence. 
The  defect  may  be  so  far  remedied  by  placing  the  object 
at  a  greater  distance  from  the  eye,  so  as  to  give  the  rays 
a  less  degree  of  divergence,  and  thus  enable  the  eye  to 
bring  them  to  a  focus  upon  the  retina.  Hence,  old 
persons  have  a  greater  difficulty  in  seeing  distinctly 
near  objects  than  those  at  a  distance.  But,  should  the 
eye  be  too  weak  even  to  accomplish  this,  a  convex  lens 
or  glass  must  be  used,  just  of  sufficient  power  to  aid  the 
eye  towards  the  proper  convergence  of  the  rays. 

Some  eyes  again  have  too  much  convergent  power, 
that  is,  they  bring  the  rays  to  a  focus  in  front  of  the 
retina.  This  condition  of  the  eye  is  called  "short- 
sightedness." Thus,  if  A  B  be  the  object  placed  before 
an  eye  of  this  kind  (fig.  55),  an  image  of  A  B  is  formed 
in  the  interior  of  the  eye  at  A'  B';  the  rays,  therefore,  in 
this  case  also,  fall  upon  the  retina  in  a  scattered  state, 
and  indistinct  vision  ensues.  If  the  object  be  placed 


I 


Fig.  55. 

nearer  the  eye,  the  divergence  of  the  rays  is  increased, 
and  may  be  made  such  as  just  to  enable  the  eye  to  form 
the  image  upon  the  retina.  Hence  short-sighted  persons 
can  see  near  objects  with  greater  distinctness  than  dis- 
tant ones. 

The  remedy  for  short-sightedness  Is  to  provide  a  con- 
cave glass,  of  such  diverging  power  as  to  give  the  eye 
8  E  E 


6G  LIGHT. 

sufficient  work  to  do  to  converge  the  rays  to  a  focus  on 
the  retina. 

The  particular  adaptation  of  spectacles  to  aid  in  vision 
will  thus  be  apparent. 

64.  Size  of  Objects — Visual  Angle. — The  size  of  the 
image  of  any  external  object  depicted  on  the  retina,  de- 
pends upon  the  distance  of  the  object  from  the  eye. 
Thus,  let  E.  represent  the  retina,  and  L  the  crystalline 
lens,  A  B  the  object  (fig.  56).  The  size  of  the  image  for 
that  distance  of  the  object  is  a b.  If,  now,  the  same  object 
be  placed  at  A' B',  its  image  becomes  reduced  to  a  b't 


Fig.  5G. 

and  if  placed  farther  away  still  at  A"B",  to  a"  I".  In  a 
word,  the  greater  the  distance  of  the  object  the  smaller 
the  image.  The  angle  A  O  B  is  called  the  visual  angle; 
in  general,  it  is  the  angle  which  the  object  subtends  at  the 
centre  of  the  crystalline  lens.  It  thus  appears  that,  50  far 
as  the  eye  is  concerned,  the  size  of  an  object  depends  upon 
the  magnitude  of  the  visual  angle. 

If,  therefore,  we  have  any  number  of  objects,  A,B,C, 
etc.  (fig.  57),  having  the  same  visual  angle,  these,  though 
in  reality  very  different  in  magnitude,  will  cast  the  same 
size  of  image  on  the  retina. 

It  thus  appears  that,  were  we  to  judge  of  the  size  of 
an  object  from  the  size  of  the  picture  formed  on  the 
retina,  we  would  judge  erroneously.  How  then,  it  may 
be  asked,  can  we  form  so  correct  a  judgment  of  the  size 
of  objects?  The  reason  is;  that  we  learn  by  habit  ancl 


PERSISTENCE  OP   IMPRESSIONS.  67 

experience  to  take  into  account  the  distance  at  which  the 
object  may  be  placed.     A  child,  for  instance,  placed  near 


Fig.  57. 

us  may  appear  under  the  same  visual  angle  as  a  man  at 
some  distance  off,  yet  we  are  in  no  way  misled  as  to  their 
comparative  sizes;  we  do  not  imagine  that  the  child  is  as 
tall  as  the  man.  We  learn  by  experience  to  combine, 
in  our  judgment,  the  distance  at  which  the  child  is  in 
reference  to  the  man;  and  thus  it  is  that  we  are  led  to 
correct  the  impressions  which  our  eyes  of  themselves 
would  convey. 

65.  Persistence  of  Impressions. — The  impression 
which  light  makes  on  the  eye  is  not  obliterated  instan- 
taneously; it  continues  for  a  short  time  after  the  cause  of 
that  impression  has  ceased  to  act.  Its  duration  is  found 
to  vary  with  different  eyes,  and  also  with  the  intensity 
and  colour  of  the  light ;  but,  in  all  cases,  its  amount  is  a 
sensible  fraction  of  a  second.  If,  therefore,  a  series  of  dis- 
tinct impressions  be  made  upon  the  eye,  which  succeed  each 
other  with  sufficient  rapidity,  these  impressions  will  be 
blended  together  and  will  produce  a  continuous  sensation. 
This  persistence  of  impression  explains  the  following 
familiar  facts :  The  glowing  end  of  a  stick  which  has  been 
thrust  into  the  fire,  when  whirled  rapidly  round,  gives 
the  appearance  of  a  continuous  circle  of  light.  A  flash 
of  lightning  is  seen  for  a  time  as  an  unbroken  track  of 
fire  in  the  heavens.  A  falling  star  presents  a  similar 


68  STEREOSCOPE. 

appearance.     So  also,  when  it  is  raining  heavy,  there 
appear  so  many  lines  of  water  falling  to  the  ground. 

On  this  principle  a  number  of  entertaining  instruments 
have  been  constructed.  The  magic  disc,  the  thaumatrope, 
the  kaleidophone,  the  wheel  of  life,  the  chromotrope  top, 
etc.,  all  owe  their  action  to  this  principle. 

66.  Irradiation. — This  is  the  phenomenon  in  virtue  of 
which   small  objects,  when   highly  illuminated,  appeal- 
larger  than  they  really  are.    It  results  from  the  spherical 
aberration  of  the  eye,  or  from  the  fact  that  there  is  an 
extension  more  or  less  of  the  image  upon  the  retina 
beyond  its  true  or  defined  outline. 

Irradiation  explains  such  facts  as  the  following : — 
"A  platinum  wire,  raised  to  whiteness  by  a  voltaic 
current,  has  its  apparent  diameter  enormously  inc 
The  crescent  moon  seems  to  belong  to  a  larger  sphe 
than  the  dimmer  mass  of  the  satellite  which  it 
clasps.     .     .     .     The  white-hot  particles  of  carbon  in 
flame  describe  lines  of  light  because  of  their  rapid,  upwa 
motion.     These  lines  are  widened  to  the  eye;  and  thus 
far  greater  apparent  solidity  is  imparted  to  the  flame  th 
in  reality  belongs  to  it."  *     So  also  a  bright  star,  such  as 
Sirius  or  the  Dog-star,  appears  larger  than  it  really  is. 

67.  Stereoscope. — In  looking  at  any  object,  the  image 
or  picture  formed  in  each  eye  is  not  the  same.     For 
example,  if  we  place  a  vase  before  us,  there  is  depicted 
on  the  retina  of  the  right  eye  an  image  of  the  vase^  and 
on  that  of  the  left  eye  also  an  image  of  the  vase ;  bui|  tjie 
former  image  is  different  from  the  latter — a  part  01  the 
vase  is  seen  by  the  right  eye  which  is  not  seen  by  the 
left,  and  a  part  is  seen  by  the  left  which  is  not  seen  by 
the  right.      If,  therefore,  pictures  be  taken  of  the  vase 
corresponding  to  the  views  of  the  individual  eyes,  these 
pictures  will  not  be  identical.    The  object  of  a  stereoscope 
is  to  combine  such  pictures,  and  thus  by  its  use  there  is 
produced  in  the  mind    the  same  impression  as  would 
result  were  the  object  actually  before  us.     Fig.  58  will 

*  Tyndall's  Notes  on  Light,  pp.  26,  27, 


STEREOSCOPIC  VIEW. 


6D 


§ 


70 


LIGHT. 


show  the  difference  which  subsists  between  the  two  pic- 
tures in  a  stereoscopic  slide. 

The  first  form  of  the  stereoscope  is  due  to  Wheatstone. 
It  consisted  of  two  plane  mirrors,  so  arranged  as  to  re- 
flect to  each  eye  the  particular  view  of  the  object  which 
belonged  to  it,  and  at  the  same  time  to  make  these  views 
coalesce.  This  is  known  as  the  "reflecting"  stereoscope. 
The  most 'familiar  form  of  the  instrument  is  the  "  len- 
ticular" stereoscope,  in- 
vented by  Brewster. 
Its  construction  and 
action  will  be  under- 
stood from  the  accom- 
panying figures.  A 
double  convex  lens 
(fig.  59)  has  its  sides, 
a,  b,  cut  away,  the  re- 
maining part  A  B  is 
then  cut  across  at  the 
middle.  The  two  halves 
are  set  in  the  instru- 
ment with  their  edges 
A,  B  in  juxtaposition, 
as  in  fig.  60. 

Now  let  C,  C'  be  the 
two  pictures  of  the  ob- 
ject placed  in  the  focus 
of  the  divided  lens,  the 
rays,  after  emerging 
from  the  glasses,  enter 
the  eyes  as  if  they  came 
from  one  picture  at  Dj 
in  other  words,  the  two 
pictures  will  overlap  or 
be  blended  together  at 
Fig.  60.  that  point,  and  thus 

there  is  produced  in  the  mind  the  impression  of  solidity  or 
relief. 


PRISMS.  71 


CHAPTER  Y. 

68.  Medium  with  Parallel  Surfaces. — When  a  ray 
of  light  passes  obliquely  through  a  plate  of  glass  with 
parallel  surfaces,  it  emerges  in  a  direction  parallel  to  the 
incident  ray.     Thus,  let 

AB  be  the  plate  (fig.  61), 
the  ray  CD  in  entering 
the  glass  is  refracted  in 
the  direction  D  E,  and 
emerges  in  the  direc- 
tion E  F,  E  F  being 
parallel  to  C  D.  A 
similar  treatment  of 
light  takes  place  with 
hollow  glass  vessels 
having  such  surfaces, 
and  containing  liquid.  Fig.  61. 

69.  Prisms — Course  of  a  Bay  through  a  Prism. — 
A  prism  in  optics  'is  a  wedge-shaped  transparent  sub- 
stance, constructed  generally  of  glass.    The  angle  enclosed 
by  the  two  oblique  faces  is  called  the  refracting  angle  of 
the  prism  (fig.  62). 

The  treatment  of  a  ray  of  homogeneous  light  by  a  prism 
is  this  :  Let  S  I  be  the  ray  (a),  and  I N  the  perpendicular 
upon  the  face  at  the  point  of  incidence;  the  ray  is  refracted 
towards  the  perpendicular,  and  follows  the  course  I  E  iii- 
side  the  prism*  On  emergence  it  is  again  refracted,  but  now 
from  the  perpendicular  upon  the  other  face,  E  N',  in  the 
direction  E  B.  Thus  the  ray  is  bent  twice  in  the  same 
direction,  that  is,  towards  the  base  of  the  prism.  If  the 
incident  ray  (6)  be  perpendicular  to  the  face  of  the  prism, 
there  is  only  one  refraction,  and  that  takes  place  at  tho 
point  of  emergence,  in  the  direction  E  R. 

If,  again,  the  incident  ray  (c)  so  fall  as  that  .the  refracted 
ray  I  E  becomes  parallel  to  the  base,  then  the  emergent 
ray  E  R  is  such  that  the  angle  R  E  N'  =  the  angle  SIN. 


72 


LIGHT. 


In  this  case  the  deviation  of  the  incident  ray  from  its 
original  course  is  the 


Fig.  62. 

70.  Dispersion. — When  a  beftm  of  solar  light  is  made 
to  pass  through  a  prism,  the  beam  is  not  only  refracted, 


DISPERSION.  73 

but  It  is  also  decomposed  or  broken  up  into  so  many  con- 
stituent parts,  a  phenomenon  which  is  called  dispersion. 

Newton  was  the  first  to  discover  this.  He  admitted  a 
sun-beam,  S,  by  an  aperture  in  the  shutter  of  a  darkened 
room,  and  allowed  it  to  fall  upon  a  prism  P  (fig.  63). 
Placing  a  screen,  E,  at  some  distance,  he  found  an  elongated 
imajje  of  the  sun  there  formed,  and  coloured  after  the 


following  manner  (commencing  from  the  lower  end) : — 
Red,  orange,  yellow,  green,  blue,  indigo,  and  violet.  In 
order  to  see  whether  there  was  any  further  decomposi- 
tion possible,  Newton  transmitted  each  of  these  colours 
separately  through  another  prism,  but  no  other  variety 
of  colour  was  obtainable.  The  red  light  gave  a  red 
image,  the  orange  an  orange  image,  and  so  on  succes- 
sively. 

Prom  such  experiments  it  has  been  inferred  that  the 
sun's  light  is  not  homogeneous,  but  consists  of  these  seven 
different  kinds  of  light,  and  these  only. 

The  elongated  coloured  image  thus  formed  by  a  prism  is 
termed  the  solar  spectrum.  The  different  colours  have 
different  amounts  of  refrangibility.  Thus  the  red  light 
is  least  refrangible,  and  therefore  takes  the  lowest  part  of 
the  spectrum ;  the  violet  light,  again,  is  the  most  refran- 


74  LIGHT. 

gible,  and  takes  the  highest  part.  Hence  arises  the 
phenomenon  of  dispersion.  Moreover,  the  colours  do  not 
occupy  an  equal  space  in  the  spectrum.  Orange  is  found 
to  occupy  the  least  space,  and  violet  the  greatest. 

71.  Curious  Facts  as  to  the  Solar  Spectrum. — Beyond 
the  limits  of  the  visible  spectrum,  in  both  directions,  there 
are  rays  which  do  not  excite  the  optic  nerve,  but  the 
existence  of  which,  though  they  are  invisible,  is  proved 
by  experiment.     There  are  rays,  beyond  the  red,  which 
have  great  calorific  or  heating  power  j  and  there  are  rays, 
beyond  the  violet,  which  possess  considerable  chemical 
power. 

The  coloured  spaces  in  the  spectrum  are  not  continuous. 
There  are  certain  interruptions  in  their  continuity,  in  the 
shape  of  a  number  of  thin  dark  lines,  which  are  distri- 
buted irregularly  throughout,  in  a  direction  perpendicular 
to  its  length.  These  lines  were  first  carefully  studied 
and  accurately  mapped  out  by  Fraunhofer,  and  hence  are 
called  Fraunhofer 's  lines. 

72.  Recomposition   of  White  Light. — Since  white 
light  can  be  broken  up  into  seven  different  colours,  it 
may  naturally  be  asked,  can  these  colours  be  so  rccom- 
bined  as  to  produce  white  light  ?     Yes  ;  they  can.     There 
are  several  ways  in  which  this  may  be  effected.     The 
following  may  be  mentioned  : — 

(1)  By  taking  another  prism  of  the  same  refracting 
angle  as  the  dispersing  one,  and  placing  it  near  the  other 
in  an  inverted  position.     The  first  prism  decomposes  the 
solar  beam  ;  the  second  reunites  the  constituent  parts  of 
it,  and  produces  a  ivhite  image  of  the  sun. 

(2)  By  allowing  the  decomposed  beam  to  fall  upon  a 
concave  mirror.     The  coloured  rays  after  reflection  are 
concentrated  in  the  focus  of  the  mirror,  and  form  there  a 
white  image,  which  may  be  received  upon  a  screen* 

(3)  By  means  of  Newton's  disc.     This  consists  of  a 
disc   of  cardboard   (fig.  64),   coloured  with   the   several 
tints,  the  different  sectors  being  made  to  correspond,  as 
far  as  possible,  with  the  proportional  spaces  of  the  colours 


DOCTRINE  OP  COLOURS. 


75 


as  they  exist  in  the  spectrum.  If  this  disc  be  made  to 
rotate  rapidly,  the  colours  are  so  blended  as  approxi- 
mately to  produce  whiteness. 


73.  Doctrine  of  Colours. — "Natural  bodies  possess 
the  power  of  extinguishing,  or,  as  it  is  called,  absorbing 
the  light  that  enters  them.  This  power  of  absorption  is 
selective,  and  hence,  for  the  most  part,  arise  the  pheno- 
mena of  colour. 

"When  the  light  which  enters  a  body  is  ivholly  absorbed 
the  body  is  black ;  a  body  which  absorbs  all  the  waves 
equally,  but  not  totally,  is  grey ;  while  a  body  which 
absorbs  the  various  waves  unequally  is  coloured.  Colour 
is  due  to  the  extinction  of  certain  constituents  of  the 
white  light  within  the  body,  the  remaining  constituents, 
which  return  to  the  eye,  imparting  to  the  body  its 
colour. 

"  It  is  to  be  borne  in  mind  that  bodies  of  all  colours, 


76  LIGHT. 

illuminated  by  white  light,  reflect  white  light  from  their 
exterior  surfaces.  It  is  the  light  which  has  plunged  to  a 
certain  depth  within  the  body,  which  has  been  sifted 
there  by  elective  absorption,  and  then  discharged  from 
the  body  by  interior  reflection,  that,  in  general,  gives  the 
the  body  its  colour.  .  .  . 

"  A  body  placed  in  a  light  which  it  is  incompetent  to 
transmit  appears  black,  however  intense  may  be  the 
illumination.  Thus,  a  stick  of  red  sealing  wax  placed  in 
the  vivid  green  of  the  spectrum  is  perfectly  black.  A 
bright  red  solution  similarly  placed  cannot  be  dis- 
tinguished from  black  ink ;  and  red  cloth,  on  which  the 
spectrum  is  permitted  to  fall,  shows  its  colour  vividly 
when  the  red  light  falls  upon  it,  but  appears  black  beyond 
this  position.  .  .  . 

"  Colour  is  to  light  what  pitch  is  to  sound.  The  pitch 
of  a  note  depends  solely  on  the  number  of  aerial  waves 
which  strike  the  ear  in  a  second.  The  colour  of  light 
depends  on  the  number  of  etherial  waves  Avhich  strikes 
the  eye  in  a  second.  .  .  . 

"  The  waves  of  the  extreme  violet  are  about  half  the 
length  of  those  of  the  extreme  red,  and  they  strike  the 
retina  with  double  the  rapidity  of  the  red.  While,  there- 
fore, the  musical  scale,  or  the  range  of  the  ear,  is  known 
to  embrace  nearly  eleven  octaves,  the  optical  scale,  or 
range  of  the  eye,  is  comprised  within  a  single  octave."* 

74.  Complementary  Colours. — One  colour  is  said  to  be 
complementary  to  another,  when  in  combination  with  that 
other  it  produces  white  light.  Thus  red  is  complementary 
to  the  colour  resulting  from  the  mixture  of  the  remaining 
constituents  of  the  spectrum,  or  to  greenish  blue ;  yellow, 
to  indigo  blue,  and  so  on. 

75.  Chromatic  Aberration. — When  white  light  passes 
through  an  ordinary  glass  lens,  there  is  also  a  certain 
amount  of  dispersion — the  lens  is  incompetent  to  bring 
the  differently  coloured  rays  to  a  common  focus,  in  conse- 
quence of  which  the  image  of  an  object  is  seen  with  a 

*  TyndaU's  Notes  on  Light,  pp.  35,  37,  38. 


CHROMATIC  ABERRATION. 


77 


coloured  border.    This  lack  of  power  on  the  part  of  a  lens 
is  called  chromatic  aberration. 


Fig.  65. 

Thus  the  lens  A  (fig.  65)  will  decompose  the  light, 
and  form  a  series  of  foci  instead  of  one — the  red  rays 
being  concentrated  at  B,  and  the  violet  ones  at  V,  whilst 
the  intermediate  rays  are  arranged  in  order. 

This  defect  in  a  lens  is  obviated  by  the  combination  of 
a  double  convex  lens  of  crown  glass,  with  a  concavo-con- 
vex of  flint  glass.  The  effect  of  the  second  lens  is  to 
re-blend  the  coloured  rays  which  the  first  has  produced, 
and  at  the  same  time  such  an  amount  of  refraction  is 
preserved  as  to  bring  the  light  to  a  focus. 

Such  a  lens  is  called  an  achromatic  lens.  It  is  much 
used  in  the  more  perfect  optical  instruments. 


78  LIGHT. 


QUESTIONS. 

1.  Explain  the  inversion  of  the  image  of  an  object  by  rays 
passing  through  a  small  aperture;  and  why  the  shape  of  the 
image  is  independent  of  the  form  of  the  aperture. 

2.  It  is  found  that  a  lamp  and  a  candle,  when  placed  respec- 
tively at  a  distance  of  5  feet  and  3  feet,  illuminate  a  screen 
equally.     Express  the  relative  intensities  of  the  two  sources  of 
light. 

3.  Explain  by  a  diagram  what  is  meant  by  the  principal  axis 
of  a  concave  spherical  mirror.     Show  also  the  position  of  the 
principal  focus. 

4.  If  a  ray  of  light  pass  from  air  into  water,  show  by  a  dia- 
gram what  course  it  pursues,  and  explain  clearly  the  expression 
the  index  of  refraction. 

5.  Sketch  (1)  a  converging,  and  (2)  a  diverging  lens.     In  using 
the  simple  microscope,  where  must  the  object  be  placed  that  a 
magnified  image  of  it  may  be  seen  ?  Is  the  image  real  or  virtual  ? 

6.  Point  out  the  causes  and  remedies  of  long  and  short  sight. 

7.  Describe  and  explain  the  stereoscope. 

8.  In  looking  at    any  object  with  both  eyes,   how  do  they 
arrange  themselves  ?    If  I  hold  up  my  linger  in  front  of  a  small 
object,  and  look  at  that  object,  I  see  two  fingers ;  or  if  I  look  at 
iny  finger,  I  see  two  objects.     Explain  this. 

9.  Enumerate  the  constituents  of  white  light.     How  was  this 
discovered,  and  by  whom  ? 

10.  What  is  meant  by  chromatic  aberration  ?    How  may  it  be 
obviated  ? 

11.  Sketch  a  prism.     Show  the  action  of  a  prism  upon  a  ray 
of  homogeneous  light. 

12.  Point  out  some  analogies  in  the  phenomena  of  sound,  light, 
and  radiant  heat. 


HEAT. 


CHAPTER  I. 

76.  Nature  of  Heat. — As  in  the  case  of  light,  there 
have  been  two  theories  brought  forward  to  explain  the 
phenomena  of  heat.     One  is  called  the  material  theory, 
and  the  other  the  dynamical  theory. 

According  to  the  material  theory,  heat  is  a  kind  of 
matter;  that  it  consists  of  an  imponderable  substance 
surrounding  the  molecules  of  bodies,  and  that  in  virtue 
of  its  attraction  for  other  matter,  and  its  repulsion  for  its 
own  particles,  it  can  readily  pass  from  one  body  to  another. 
According  to  the  dynamical  theory,  heat  is  an  affection  or 
condition  of  matter  ;  that  the  heat  of  a  body  is  caused  by 
a  vibratory  motion  among  its  particles ;  further,  that  the 
molecules  of  warm  bodies  possess  the  power  of  communi- 
cating a  vibratory  motion  to  the  surrounding  ether,  in 
virtue  of  which  contiguous  bodies  may  be  heated.  Very 
hot  bodies  are,  on  this  hypothesis,  those  which  give  a 
rapid  vibratory  motion  to  the  all-pervading  ether.  The 
latter  theory  is  the  one  more  generally  accepted  by 
modern  physicists. 

77.  Heat  and  Cold. — The  ordinary  sensations  which 
are  familiarly  known  as  heat  and  cold,  are  merely  different 
degrees  of  the  same  influence.    If  we  touch  in  succession, 
for  example,  two  similar  bodies  unequally  heated,  the  one 
may  appear  to  the  hand  cold,  the  other  hot ;  but  these 
sensations  are  due  to  the  fact  that  the  bodies  have  different 
amounts  of  the  same  influence,  viz.,  heat. 

78.  General  Effect  of  Heat,— The  most  general  effect 


80  HEAT. 

of  heat  on  a  body  is  to  expand  it,  or  cause  an  enlarge- 
ment of  its  volume.  If  heat  be  abstracted  from  a  body, 
or  the  body  be  cooled  down,  the  contrary  effect  ensues — 
the  volume  of  the  body  is  diminished.  Hence  we  have 
the  general  principle  (to  which,  however,  there  are  some 
exceptions),  that  heat  expands  and  cold  contracts.  These 
effects,  arising  either  from  an  increase  or  diminution  of 
temperature,  are  produced  in  very  different  degrees,  ac- 
cording to  the  nature  of  the  bodies.  They  are  small  in 
solids,  greater  in  liquids,  and  still  greater  in  gases. 

79.  Expansion  of  Solids. — The  expansion  which  a 
body  undergoes,  in  regard  to  length,  is  called  linear ; 
in  regard  to  surface,  superficial ;  and  in  regard  to 
volume,  cubical,  expansion. 

To  illustrate  linear  expansion,  the  following  apparatus 
has  been  devised  (fig.  67): — 


Fig.  67. 

A  metallic  bar  is  supported  on  pillars,  as  in  the 
figure.  Its  free  end  presses  upon  a  lever,  which  in 
turn  acts  upon  an  index,  playing  over  a  graduated 
arc.  By  this  arrangement  a  multiplying  effect  is  pro- 
duced upon  the  index,  in  consequence  of  ^which  the 
smallest  elongation  on  the  part  of  the  bar  is  rendered 

manifest. 

The  cubical  expansion  of  a  body  is  shown  very  simply 
thus  :  A  small  brass  ball  (fig.  68)  just  passes  through 
an  aperture  in  a  metal  plate  supported  on  three  legs. 


CO-EFFICIENT    OF    EXPANSION. 


81 


When  the  ball  is  heated  by  being  held  over  a  spirit  lamp, 
it  refuses  to  go  through  the  aperture,  and  will  not  do  so 
until  it  regains  its  former  temperature. 


Fig.  68. 

80.  The  Co-efficient  of  Expansion. — The  co-efficient  of 
expansion  (linear,  for  instance),  may  be  denned  to  be  that 
fraction  of  a  body's  length  which  it  expands  on  being  heated 
1°  centigrade.  The  co-efficients  of  many  substances  have 
been  carefully  determined  by  experiment.  The  following 
table  may  be  given  as  a  specimen  : — 

CO-EFFICIENTS  OF  EXPANSION  (LINEAR). 

Zinc -0000294  Gold -0000146 

Silver -0000190  Iron -0000123 

Brass '00001 88  Platinum -0000088 

Glass -0000080 

It  is  easily  proved  that  the  superficial  is  double  of  the 
linear  co-efficient,  and  that  the  cubical  is  treble. 

From  this  table  it  appears  that  zinc  is  the  most  expan- 
sible metal,  and  platinum  the  least ;  also  that  the  expan- 
sibility of  platinum  and  glass  is  nearly  the  same.  Hence 

8E  F 


HEAT. 

the  reason  why  a  chemist  can  fuse  a  platinum  wire  into 
a  glass  tube  without  liability  to  fracture. 

81.  Practical  Applications. — The  principle  of  expan- 
sion or  contraction  is  utilized  much  in  practice.     The 
hoop  of  iron  by  which  a  wheel  is  surrounded,  is  made 
of  the  same  diameter  as  the  wheel.     It  is  then  heated, 
and  in   this   state   is    put   011   the   wheel.      The  whole 
being  thrown  into  water,  the  iron  hoop  contracts  with 
great  force,  and  thus  binds  the  spokes  and  rim  firmly 
together.      A  similar  method   is  employed  for  binding 
together  the  staves  of  'tubs,  vats,  barrels,  etc.     The  walls 
of  a  building  have  been  restored  to  their  perpendicular 
position  by  taking  advantage  of  the  enormous  contractile 
force  of  iron. 

In  the  combination  of  metallic  pipes,  by  which  water 
is  brought  from  great  distances  for  the  supply  of  towns, 
means  must  be  provided  for  allowing  expansion  or  con- 
traction to  take  place  freely.  Hence  the  pipes  are  so 
constructed  as  to  be  capable  of  sliding  one  within  the 
other,  after  the  manner  of  the  joints  of  a  telescope.  In  all 
iron  bridges,  similar  precautions  are  necessary;  they  are 
generally  supported  on  friction  rollers. 

The  same  principle  explains  certain  familiar  facts. 
Thus,  when  hot  water  is  poured  into  a  cold  glass  vessel, 
fracture  often  takes  place.  This  arises  from  the  un- 
equal expansion  of  the  glass,  the  heat  not  having  had 
sufficient  time  to  extend  its  influence  equally  to  other 
parts  of  the  vessel.  The  same  accident  may  take  place 
when  cold  water  is  poured  into  a  warm  glass  vessel. 
When  the  stopper  of  a  decanter  becomes  firmly  fixed, 
it  is  not  imusual  to  wrap  a  cloth  steeped  in  hot  water 
round  the  neck,  the  neck  thereby  expands,  and  the  stop- 
per is  freed  from  its  hold. 

82.  Breguet's  Metallic  Thermometer.— :That  metals 
exhibit    different     amounts    of    expansibility    may    be 
illustrated  by  the  following  experiment :  —  Two  strips 
of   iron    and    brass    are    firmly    riveted    together   (fig. 
69).       At    the    ordinary    temperature    the    combined 


GRIDIRON    PENDULUM. 


83 


\1 


strip  is  perfectly  straight,  but  when  heated  it  becomes 
bent.  If  cooled  below  its  ordinary  tem- 
perature it  also  becomes  bent,  but  in  the 
opposite  direction.  The  experiment  de- 
monstrates, therefore,  the  greater  expansi- 
bility or  contractibility  of  brass  than  iron. 

On  the  same  principle  is  founded 
Breguet's  metallic  thermometer,  repre- 
sented in  fig.  70.  Three  strips  of  silver, 
gold,  and  platinum,  are  rolled  into  a 
very  thin  metallic  ribbon.  This  ribbon 
is  coiled  into  a  spiral  form,  and  adjusted  as 
in  the  figure,  the  internal  face  being  the 
silver  and  the  external  the  platinum.  As 
the  temperature  rises  the  spiral  unwinds 
itself;  as  it  falls,  it  moves  in  the  Kg.  69. 
opposite  direction,  and  these  changes  affect  the  index 
which  plays  over  the  graduated  circle. 

83.  Gridiron  Pendulum.— In  the  finer  kinds  of  clocks 
the  variation  of  tempera- 
ture is  guarded  against  lay 
the  use  of  what  is  called 
a  compensation  pendulum. 
A  common  form  is  the 
"gridiron"  pendulum  repre 
seiited  in  fig.  71.  It  con- 
sists of  a  combination  of 
steel  and  brass  rods,  S,  B, 
arranged  alternately,  and  of 
such  length  as  that  the  expan- 
sion or  contraction  of  the 
steel  rods  may  be  exactly 
neutralized  by  the  expansion 
or  contraction  of  the  brass 
ones.  To  the  middle  steel 
rod  is  attached  the  bob  C.  Fig  70. 

To  illustrate  its  action,  let  O  be  the  centre  of  oscilla- 
tion of  the  pendulum,  or,  which  is  the  same  thing,  let  AO 


84 


HEAT. 


be  the  length  of  the  equivalent  simple  pendulum.     In 
.A  summer  the  steel  rods  will  expand, 

I and  thus  tend  to  lower  the  point  O, 

or  lengthen  the  pendulum;  but 
the  brass  rods  also  expand,  and,  by 
their  so  doing,  they  tend  to  raise 
the  point  O,  or  shorten  the  pen- 
dulum. If,  therefore,  the  point  O 
is  as  much  raised  by  the  expansion 
of  the  brass  rods  as  it  is  depressed 
by  the  expansion  of  the  steel  ones, 
it  will  be  kept  in  the  same  position, 
in  other  words,  the  length  AO  will 
be  unchanged.  In  winter,  in  like 
manner,  if  the  effects  of  contraction 
in  the  one  case  be  equal  to  the  effects 
of  contraction  in  the  other,  the 
length  of  the  pendulum  will  be  pre- 
served. Hence,  by  this  arrangement, 
the  pendulum  is  kept  constant  in  its 
length. 

84.  Exceptions  to  Expansion. — 
There  are  some  exceptions^  the  prin- 
ciple of  expansion  by  heat  which  are 
worthy  of  notice. 

In  what  is  called  "  Rose's  fusible  metal,"  which  is  an 
alloy  of  bismuth,  lead,  and  tin,  in  certain  proportions,  the 
expansion  is  nearly  uniform  from  32°  to  110°  Fahrenheit, 
but  at  this  point  the  expansion  ceases,  and  as  the  tem- 
perature rises  to  about  155°  it  undergoes  a  constant 
contraction. 

There  are  some  crystals  which,  when  heated,  expand  in 
one  direction,  but  contract  in  another. 
'  '  But,  perhaps,  the  most  singular  exception  is  found 
in  the  case  of  india-rubber.  A  piece  of  stretched 
india-rubber,  on  being  heated,  contracts.  This  sub- 
stance also  forms  an  exception  to  the  all  but  general 
rule,  that  when  a  body  is  stretched,  cold  is  developed. 


Fig.  71. 


EXPANSION   OP   LIQUIDS.  85 

If  a  wire,  for  example,  be  lengthened,  its  temperature 
is  lowered ;  not  so  with  india-rubber,  a  stretched  piece 
of  rubber  is  found  to  have  its  temperature  raised. 


CHAPTER  II. 


85.  Expansion  of  Liquids. — The  expansion  of  a  liquid, 
such  as  water,  may  be  proved 
by  the  following  experiment : 
Take  a  narrow  tube  (fig.  72.) 
with  a  large  bulb  at  its  ex- 
tremity, fill  the  bulb  and  part 
of  the  tube  with  coloured  water. 
If  now  the  bulb  be  heated  by 
a  lamp  the  water  begins  to  ex- 
pand, and,  owing  to  the  great 
difference  of  capacity  between 
the  bulb  and  the  tube,  any 
small  expansion  is  rendered 
manifest  by  a  considerable  rise 
of  the  liquid  in  the  tube ;  and 
in  a  short  time  it  will  reach 
the  top. 

Tho    co-efficient   of   expansion 
of    a    liquid   (having    reference 
of    course   to   cubical   dilatation 
only)  is,  as  before,  that  fraction 
of     its    volume    which    it    ex- 
pands   011    being    heated     1°C.  Fig.  72. 
Of  all   liquids  which   have   been   subjected   to   experi- 
mental investigation,   there  are  none  which  have  been 
more    thoroughly    examined   than   water,   alcohol,   and 
mercury. 


86  HEAT. 

The  following  co-efficients  have  been  determined  in 
regard  to  them  : — 

CO-EFFICIENTS  OF  EXPANSION  BETWEEN  Oe  AND  100°  C. 

Alcohol -00116 

Water '000466' 

Mercury '000154. 

The  expansion  of  these  liquids,  however,  is  not  perfectly 
uniform;  there  is  found  to  be  great  irregularity  near 
their  boiling  points.  In  the  case  of  mercury,  its  expan- 
sion is  nearly  uniform  between  the  limits  of-36°C.  and 
100°C. 

86.  The  Thermometer. — In  consequence  of  the  uniform 
expansion  of  mercury,  and  its  great  sensitiveness  to  heat, 
it  is  the  fluid  more  generally  used  in  the  construction  of 
the  thermometer — the  common  instrument  for  indicating 
temperature. 

The  mercurial  thermometer^  consists  of  a  tube  with  a 
small  uniform  bore,  terminating  in  a  bulb.  The  bulb  and 
part  of  the  tube  are  filled  with  mercury,  in  such  quantity 
as  that  the  mercury  may  neither  pass  wholly  into  tho 
bulb,  nor  reach  the  top  of  the  tube,  when  subjected  to 
the  ordinary  extremes  of  cold  or  heat.  The  graduation 
of  the  instrument  is  effected  in  the  following  manner  : — 
Two  invariable  or  fixed  points  are  selected,  viz.,  the 
freezing  point,  and  the  boiling  point  of  water  at  the  sea 
level,  and  under  the  mean  pressure  of  the  atmosphere. 
The  former  point  is  obtained  by  plunging  the  tube  into 
melting  ice,  when  the  column  gradually  sinks,  and 
eventually  comes  to  rest;  the  lowest  level  of  the  mercury 
is  then  marked  off  on  the  scale  attached  to  the  tube. 
The  latter  point  is  determined  by  placing  the  instrument 
in  boiling  water,  or  in  the  steam  escaping  from  it;  this 
being  done  the  mercury  rises,  and  finally  settles  at  a 
certain  height  —  the  highest  level  attained  is  marked 
off  as  before.  The  interval  between  the  two  fixed 

*  For  the  construction  of  the  instrument,  see  Appendix, 
Question  12,  p,  139. 


THERMOMETRIC   SCALES.  87 

points  thus  determined  is  then  divided  into  so  many 
equal  parts. 

87.  Thermometric   Scales.  — The  interval  just  men- 
tioned is  differently  divided  in  different  countries,  giving 
\ise  to  the  three  common  forms  of        F  c  R 
the  thermometer.    These  are  named 

from  the  inventors,  and  are  known 
as  the  Fahrenheit,  Celsius  or  centi- 
grade, and  Reaumur.     In  Fahren- 
heit (fig.  73)  the  freezing  point  is 
marked  32  (a  zero  being  taken  which 
was  incorrectly  imagined  to  be  the     32--J          0- 
greatest  cold  obtainable),  and  the 
boiling  point  212;    in   centigrade       ®          <&          O 
these    points    are    marked   respec-  Fig.  73. 

tively  0  and  100;  and  in  Reaumur,  0  and  80.  The  space 
therefore  between  the  two  fixed  points  is  divided  in  F. 
into  180  equal  parts,  in  C.  into  100,  and  in  R.  into  80. 
Each  of  these  parts  is  called  a  degree. 

A  temperature  below  0°  in  any  of  the  scales,  is  indi- 
cated by  a  minus  placed  before  the  number.  Thus  -  10°C., 
indicates  10  degrees  below  the  freezing  point  according 
to  the  centigrade  scale;  and  again,  -  10°F.,  10  degrees 
below  0°  according  to  the  Fahrenheit  scale. 

88.  Conversion  from  one  Scale  to  another — Examples. 
— The  student  will  have  little  difficulty  now  in  under- 
standing the  mode  of  converting  any  number  of  degrees 
of  one  scale  into  its  equivalent  in  another.     The  follow- 
ing examples  may  be  given  in.  illustration  : — 

Ex.  1. — Convert  68°  F.  into  the  centigrade  scale. 

The  freezing  point  being  marked  32  in  Fahren- 
heit and  0  in  centigrade,  we  must  make  allowance 
for  this  by  first  subtracting  32  from  68;  the  re- 
mainder is  36.  Now  as  180°F.  =  100°C.,  we 
have  therefore  to  state  (by  the  common  rule  of 
three)  as  follows:— ISO  :  36  : :  100  =  20;  hence 
68°  F.  =  20°C.— Ans. 

Ex.  2. — How  many  degrees  of  F.  are  equal  to  -  40°  C.  1 


HEAT. 


Here   we   must   state   the  proportion   thus: — 
100  :  -  40  : :  180  =  -  72.     Adding  32  we  have 

-  72  +  32  =  -  40;  hence  -  40°C.  =  -  40°  F.— Ans. 
Ex.  3. — How  many  degrees  of  R.  are  equal  to  100°F.? 

*100  -  32  -  68.      Then  180  :  68  : :  SO  =  30f  °  j 
hence  100°F.  -  30  f°R— Ans. 
Ex.  4. — Convert-  30 °E.  into  Fahrenheit. 

80  :  -  30  :  :  180  =  -  67J.     Adding  32  *  we  have 

-  67 J  +  32  -  -  35J ;  hence  -  30°  R  =  -  35J°F.— 
Ans. 

89.  Ebullition. — The  process  by  which  water  is  raised 
to  the  boiling  point  is  a  very 
interesting  one.  Thus,  let 
an  open  flask  of  water  be 
exposed  to  heat,  as  in  fig.  74. 
The  stratum  of  fluid  at  the 
bottom,  in  becoming  heated, 
expands  and  rises  towards  the 
surface;  another  stratum  tak- 
ing its  place  in  like  manner 
expands  and  rises,  and  so  on 
successively.  There  are  pro- 
duced therefore  in  the  vessel 
a  series  of  ascending  warm 
currents  and  of  descending- 
colder  currents,  and  this  cir- 
culation continues  until  the 
water  is  nearly  brought  to 
the  boiling  point.  When  this 
point  is  reached,  bubbles  of  gas 
are  observed  to  form  them- 
selves next  the  heating  source. 
These  at  first,  in  their  passage 
Fig.  74.  upwards  through  the  colder 

*  The  student  will. notice  therefore  that  in  the  conversion  of 
Fahrenheit  degrees  into  centigrade  or  Reaumur,  he  must  first 
subtract  32  from  the  number  given  before  stating  the  proportion, 
and  in  the  converse  problem  add  32  after  he  has  worked  the 
proportion. 


BOILING   POINT.  89 

water  above,  are  gradually  condensed,  and  diminishing 
in  volume  as  they  ascend  scarcely  reach  the  surface ;  but 
in  proportion  as  the  whole  water  approaches  the  boiling 
point  this  condensation  ceases,  and  the  bubbles  escape 
at  the  surface  as  steam.  The  water  is  then  said  to 
boil. 

90.  The  Dependence  of  the  Boiling  Point  upon 
External  Pressure. — The  temperature  at  which  water 
boils  in  an  open  vessel  is  dependent  upon  the  pressure  of 
the  atmosphere.  At  the  ordinary  pressure,  that  is,  when 
the  barometer  indicates  about  30  inches  of  mercury,  the 
boiling  point  is  212°F.  Bub  if  the  pressure  diminish  the 
boiling  point  falls,  and,  on  the  other  hand,  if  the  pressure 
increase  it  rises  above  the  temperature  of  212°.  Hence 
the  necessity  of  strictly  denning  what  the  boiling  point  of 
a  liquid  really  is.  It  is  that  point  of  temperature  at 
which  the  tension  or  elastic  force  of  its  vapour  is  exactly 
equal  to  the  pressure  it  supports. 

The  variation  of  the  boiling  point  of  water  with  tho 
pressure  will  be  seen  from  the  following  table  : — 

Height  of  the  Barometer.  Boiling  Point. 

(Inches).  (Fahrenheit). 

17-04     185°. 

18-99     190°. 

21-12     ,  195°. 


23-45 
25-99 

28-74 
29-33 


200°. 
205°. 
210°. 
211°. 


29-92     212°. 

30-51     213°. 

31-73     215°. 

From  this  table  it  appears  that  a  variation  of  -^  of  an 
inch  of  the  barometer  causes  a  difference  of  about  -J-  of  a 
degree  Fahernheit  in  the  boiling  point ;  hence  the  range 
of  the  boiling  point  in  our  climate  may  be  as  much  as  5°, 
with  the  ordinary  variations  of  the  barometer. 

In  a  closed  vessel,  water  may  be  raised  to  a  much 
higher  temperature  than  212°.  This  is  the  case  in  the 


90 


HEAT. 


boiler  of  a  steam-engine,  or  of  a  locomotive.  By  tho 
accumulation  of  the  steam  the  pressure  on  the  water  is 
increased,  the  boiling  point  is  therefore  raised,  or  the 
water  is  heated  above  its  ordinary  boiling  point. 

91.  -Illustrations. — A  striking  illustration  of  the  de- 
pendence of  the  boiling  point  upon  external  pressure,  is 
to  take  a  vessel  of  hot  water,  put  it  under  the  receiver  of 
the  air  pump,  and  exhaust  the  air.  In  a  short  time  the 
water  begins  to  boil,  and  as  the  rarefaction  goes  on,  the 
ebullition  increases  in  intensity. 

Another  experiment  consists  in  taking  a  vessel  of  hot 
water  (fig.  75),  corking  it  up,  and  then  inverting  it.  If  now 


Fig.  75. 

cold  water  be  allowed  to  fall  over  the  confined  vapour,  it 
partially  condenses  it;  the  water  in  the  vessel  therefore  is 
so  far  relieved  from  pressure,  and  in  consequence  enters 
into  a  state  of  ebullition. 


DEPORTMENT   OF  WATER  IN   FREEZING. 


91 


92.  Maximum  Density  of  [Water. — If  a  quantity  of 
water,  say  at  the  temperature  of  62°F.  (standard  temp.), 
be  gradually  cooled  down,  it  contracts  until  it  reaches  the 
temperature  of  39°,  when  all  further  contraction  ceases. 
This   point   is   called   the   point  of  maximum   density. 
When  cooled  below  this  temperature  expansion  sets  in, 
which  increases   rapidly   as    the    freezing   point   is   ap- 
proached.   Water  is  therefore  heaviest  at  the  temperature 
of  39°  F.  or  4°  C.     For  example,  a  cubic  foot  of  water 
at  that  temperature  weighs  more  than  a  cubic  foot  at 
any  other  temperature. 

93.  Deportment  of  Water  in  Freezing. — When  water 
freezes,  it  undergoes  a  sudden  expansion.    The  amount  of 
its  expansion  is  found  to  be  about  10  per  cent. ;  more 
exactly,  1000  cubic  feet  of  water  at  the  freezing  point 
become  1102  cubic  feet  of  ice  at  the  same  temperature. 


Fig.  76. 

The  force  of  this  expansion  is  almost  irresistible.  A 
strong  iron  bottle  filled  with  water,  and  firmly  closed, 
when  immersed  in  a  freezing  mixture,  is  rent  asunder  in 
a  short  time.  Some  interesting  experiments  on  this 
point  were  made  one  severe  winter  at  Quebec  by  Major 


92  HEAT. 

"Williams.  He  took  a  bomb-shell,  and  having  filled  it 
with  water,  carefully  plugged  up  the  aperture ;  on  expos- 
ing it  to  the  frost,  the  plug  was  driven  to  a  distance  of 
330  feet,  whilst  at  the  same  time  a  cylinder  of  ice  8|- 
inches  long  appeared  protruding  at  the  aperture  (fig.  76). 
In  another  experiment,  the  plug  being  more  firmly  fixed, 
the  bomb  was  ruptured  at  the  middle,  and  a  ring  of  ice 
was  forced  through  the  rent. 

The  common  accident  of  the  bursting  of  pipes  in  frosty 
weather,  can  therefore  be  easily  understood.  The  rupture 
takes  place,  of  course,  during  the  frost ;  but  the  rent  being 
closed  up  with  ice,  no  leakage  of  water  takes  place.  It 
is  only  when  the  thaw  sets  in  that  the  damage  done  to 
the  pipe  becomes  apparent. 

94.  Effects  in  Nature. — In  the  economy  of  nature  the 
expansion  which  accompanies  the  freezing  of  water  exerts 
a  most  important  agency.  Had  water,  in  cooling,  observed 
the  general  law  of  contraction,  then  a  layer  of  ice  when 
formed  on  the  surface  of  our  lakes  or  rivers  would  have 
sunk  to  the  bottom ;  another  would  have  been  formed, 
and  in  like  manner  have  sunk  to  the  bottom,  and  so  on 
until  the  whole  water  had  become  one  solid  mass  of  ice, 
which  all  the  influence  of  a  summer  sun  could  scarcely 
have   dissolved.      As  it   is,   however,   these   effects  are 
happily  prevented.     The  ice  being  lighter  than  the  water 
floats  on  the  surface,  and  thus  the  water  below,  being 
sheltered  from  the  cold  atmosphere  above,  preserves  its 
liquid  form. 

It  is  thus  also  that  our  soils  are  pulverized  during 
winter.  The  water  they  imbibe,  upon  freezing,  disinte- 
grates them,  and  thereby  assists,  in  no  small  degree,  the 
labours  of  the  husbandman  in  preparing  them  for  the  re- 
ception of  the  seed.  Hence,  during  frost,  the  soil  is 
observed  to  have  a  cracked  appearance. 

95.  Expansion   on  Solidification — a  Property  not 
Peculiar   to  Water. — There  are  certain   metals   which, 
in   passing   from  a  state  of  fusion  into  the  solid  form, 
manifest  the  same  deportment  as  water;  they  expand  on 


EXPANSION   OF   GASES.  93 

solidifying.  These  are,  cast-iron,  bismuth,  and  antimony. 
Hence  the  precision  with  which  cast-iron  takes  the  im- 
pression of  a  mould. 


CHAPTER  III. 

96.  Expansion   of  Gases. — The  expansion  of  gases 
exceeds  that  of  either  solids  or  liquids,  and  is  almost 
uniform;  that  is,  the  amount  of  expansion  is  found  to 
be  nearly  in  proportion  to  the  increase  of  temperature. 
The  process  of  dilatation,  or  contraction  of  gases,  does  not 
take  place  in  the  same  manner  as  in  solids  and  liquids. 
Let  us  suppose,  for  instance,  that  we  have  a  glass  receiver 
closed  on  all  sides,  and  filled  with  air  of  the  same  density 
as  that  of  the  external  atmosphere.     If  the  temperature 
of  this  enclosed  air  be  lowered,  it  will  not  contract  in  its 
dimensions,  it  will  still  occupy  the  whole  of  the  receiver, 
but  its  elastic  force  is  reduced;  in  other  words,  it  will  not 
exert  the  same  pressure  on  the  containing  vessel  as  before, 
and  were  the  external  pressure  of  the  air  allowed  to  act, 
it  would  force  the  confined  air  into  a  smaller  space.     In 
like  manner,  suppose  the  air  contained  in  the  receiver  to 
be  subjected  to  an   increase  of  temperature,  then   the 
elastic  force  of  the  air  is  increased,  and  were  the  receiver 
to  offer   no  resistance,  it  would  expand  and  occupy  a 
greater  space.     By  gases  expanding  or  contracting  by  a 
change  of  temperature,  is  therefore  meant  that  they  do 
so  under  a  given  pressure — the  pressure  generally  taken 
being  the  ordinary  pressure  of  the  atmosphere. 

97.  Experimental    Illustrations.  —  (1)   A   bladder 
partly  filled  with  air  and  closed  up,  when  held  before 
a  fire,  becomes  gradually  inflated,  shrinking  to  its  former 
dimension  on  its  removal.     (2)  When  a  flask  of  water, 
as  in  (fig.  73),  is  at  first  heated,  bubbles  of  air  are  seen  to 
rise  through  the  water,  owing  to  the  expansion  of  the  air- 
particles  which  have  been  absorbed  by  the  water.     This 


94  HEAT. 

is  more  strikingly  seen  with  ale  or  other  fermented  liquor : 
a  quantity  of  froth  collects  on  the  surface  in  propor- 
tion as  the  gaseous  particles  are  liberated.  Hence,  when 
a  bottle  of  such  liquid  is  placed  before  a  fire,  it  often  happens 
either  that  the  bottle  is  broken,  or  the  cork  driven  out 
with  a  loud  report.  (3)  A  flask,  A,  containing  air,  is 
taken  (fig.  77),  from  which  a  bent  tube  is  led  to  a  dish 


B  filled  with  coloured  water.  Over  the  end  of  this 
tube  is  placed  an  upright  tube  C,  previously  filled 
with  the  fluid  and  inverted.  If  now  the  flask  be 
heated  by  a  spirit  lamp,  the  air  inside  expands, 
passes  through  the  bent  tube,  and  collecting  in  C, 
gradually  displaces  the  fluid,  and  eventually  expels  it 
entirely. 

98.  Fire-Balloon. — In  the  experiment  just  mentioned, 
it  is  manifest  that  the  air  thus  expanded  is  lighter, 
bulk  for  bulk,  than  the  air  of  the  external  atmo- 
sphere. If  therefore  we  were  to  take  a  balloon  and 
fill  it  with  heated  air,  it  would  ascend  and  remain  in 


CONSTANCY   OP   THE   CO-EFFICIENT   OF   EXPANSION.       95 

an  elevated  position  so  long  as  the  heat  of  the  air  is 
preserved.  Such  is  the  principle  of  the  so-called  "  fire- 
balloon." 

99.  Constancy  of  the  Co-efficient  of  Expansion. — The 
co-efficient  of  expansion  is  found  to  be  nearly  the  same  in 
all  gases.     Its  amount  may  be  taken  at  '00366,  or  about 
-jj^-g-  of  its  volume.     Thus  1  cubic  foot  of  gas  at  0°C. 
becomes   l^r^-  cubic  feet  when  raised  1°C.,  l^-f-g-  cubic 
feet  2°0.,  I^TF  cubic  feet  5°C.,  etc.  (the  pressure  on  the 
envelope  containing  the  gas  being  preserved  constant). 
Slight  deviations  from  the  general  rule  of  constancy  in 
the  co-efficient  occur  in  the  cases  of  carbonic  acid  and 
sulphurous  acid  gases.     This  is  owing  probably  to  their 
capability  of  being  liquefied. 

100.  Physical  Character  of  Carbonic-  Acid  and  Sul- 
phurous Acid  Gases — 

(1)  Carbonic  Acid  (C02).     This  gas  is  one-half  heavier 
than  common  air,  it  is  colourless,  but  possesses  a  slight 
odour,  and  a  perceptibly  sour  taste.   Its  principal  chemical 
feature  is  that  it  extinguishes  flame,  and  causes  death  to 
an  animal  inhaling  it.     It  is  present  in  the  atmosphere, 
and  in  the  water  of  many  mineral  springs.    The  quantity 
present  in  free  air  is  nearly  constant,  amounting  to  about 
4  volumes  in  10,000  of  air.     Small  as  this  appears  to  be, 
it  is  nevertheless  sufficient  and  necessary  for  the  support 
of  vegetable  life. 

Carbonic  acid  is  given  off  by  animals  in  respiration 
and  by  combustion.  Fermented  liquors,  soda  water,  etc., 
owe  their  sparkling  briskness  to  the  escape  of  this  gas. 
It  may  be  liquefied  at  a  pressure  of  about  36  atmospheres. 
The  liquid  possesses  the  remarkable  property  of  being 
more  expansible  than  the  gas  itself — a  strange  exception 
to  the  rule  that  liquids  expand  less  by  heat  than  gases. 

(2)  Sulphurous  Acid  (SO2)  is  given  off  when  sulphur 
is  burnt,  and  in  large  quantities  from  volcanoes.     It  is 
colourless,  but  possesses  a  suffocating  smell  of  burning 
sulphur.     It  is  2|-  times  as  heavy  as  air,  and  is  reduced 
to  a  liquid  at  a  pressure  of  two  atmospheres,  or  by  being 


96  HEAT. 

cooled  down  to-10°C.  under  the  ordinary  atmospheric 
pressure. 

101.  Draft  of  Chimneys — Ventilation. — When  a  fire 
is  kindled  in  a  room,  the  flame  and  warm  smoke  pro- 
ceeding from  it  soon  raise  the  temperature  of  the  air  in 
the  chimney.  The  consequence  is  it  ascends,  and  the 
colder  air  from  the  room  flows  in  to  supply  its  place;  this 
air,  in  turn  likewise  becoming  heated,  rises,  and  a  fresh 
accession  of  air  takes  place,  and  so  on. 

What  constitutes,  therefore,  the  draft  of  a  chimney  is 
nothing  else  than  the  colder  air  of  the  room  constantly 
passing  towards  the  fire-place. 

As  the  air  in  a  room  is  continually  passing  towards  the 
fire,  there  must  of  course  be  a  constant  supply  kept  up 
from  the  external  air,  which  must  therefore  have  suffi- 
ciently free  access  by  the  doors  and  windows  of  the  house. 
Hence  it  is  found  that  in  a  house  where  the  passage  of 
the  external  air  is  much  interrupted,  the  chimneys  are 
liable  to  smoke,  the  reason  being  that  a  suflicient  draft  is 
not  maintained. 

At  the  door  of  a  room  where  there  is  a  fire  there  are 
two  opposite  currents  of  air,  the  heated  air  in  the  room 
ascends  to  the  top  and  passes  out  at  the  upper  part  of  the 
door,  whilst  the  colder  air  from  without  enters  by  the 
lower  part.  This  may  be  easily  proved  by  placing  a 
lighted  taper  in  these  positions  at  the  outside  of  the  room 
door.  In  the  former  position  the  flame  is  bent  from  the 
door,  and  in  the  latter  towards  it. 

When  all  the  windows  and  doors  of  a  house  fit  so 
closely  as  to  impede  a  communication  with  the  external 
air,  and  thus  prevent  a  sufficient  supply  for  the  fires  in 
the  house,  the  necessary  quantity  descends  by  those 
chimneys  which  are  not  in  use.  Hence,  when  a  fire  is 
being  lighted  in  any  of  these,  the  smoke  at  first  is  driven 
into  the  room.  To  remedy  this  the  room  door  ought  to 
be  shut,  or  the  window  opened;  this  being  done,  the 
chimney  will  soon  begin  to  draw.  What  is  called  lack 
smoke  in  a  room  where  there  is  no  fire  arises  from  the 


GENERAL  CHARACTER  OF  WINDS. 


97 


circumstance  that  that  chimney  is  serving  as  an  inlet  for 
air  to  supply  the  fires  in  the  house,  carrying  the  smoke 
of  a  neighbouring  chimney  down  into  the  room  along 
with  it. 

The  grand  object  in  ventilation  is  to  allow  the  heated 
air,  or  air  vitiated  by  respiration,  to  escape  at  the  roof  of 
the  building,  whilst  provision  is  made  at  the  same  time 
for  the  inlet  of  fresh  air,  the  whole  arrangements  being 
such  as  to  obviate  drafts.  The  principle  of  ventilation  is 
strikingly  illustrated  by  the  following  simple  experiment : 
A  glass  receiver  (fig.  78)  with  an  aperture  at  the  top,  is 
placed  over  a  candle  put 
into  a  flat  dish,  in  which 
there  is  water.  In  a  short 
time  the  air  in  the  receiver 
becomes  vitiated  by  the 
combustion,  and  the  candle 
flame,  gradually  dwindling 
down,  is  at  last  extin- 
guished. If,  however,  the 
candle  be  relit  and  a  card 
be  placed  in  the  funnel, 
or  chimney,  thus  dividing- 
it  into  two  parts,  the 
candle  continues  to  burn, 
preserving  its  brightness 
almost  unimpaired.  The 
reason  of  this  is,  that  the  vitiated  air  now  escapes 
through  one  of  the  passages,  whilst  fresh  air  gets  in  by 
the  otner,  as  indicated  by  the  arrows. 

102.  "Winds — General  Character  of. — The  phenomena 
of  winds,  in  general,  result  from  the  unequal  distribution 
of  heat  over  the  earth's  surface.  It  is  ascertained,  for 
example,  that  the  mean  temperature  at  the  equator  is 
84°F.,  at  78°  north  latitude  16°F.,  and  at  the  pole  it 
has  been  inferred  to  be  about  4°F.  From  such  diver- 
sity, then,  of  temperature  in  different  portions  of  the 
earth's  surface,  it  is  impossible  that  the  atmosphere  gan 

8  E  G 


98  HEAT. 

remain  calm  and  unaffected.  When  any  region  becomes 
more  heated  by  the  sun's  beams  than  some  other,  the 
air  above  it  also  gets  heated  and  rises  up,  whilst  the 
colder  surrounding  air  rushes  in  to  supply  its  place,  and 
the  atmosphere  is  more  or  less  disturbed.  Hence  arise 
those  perturbations  to  which  we  give  the  name  of 
"winds." 


r 


S.  &0 

Fig.  79. 

The  accompanying  illustration  (fig.  79)  gives  a  general 
view  of  the  character  of  the  winds  which  prevail  in  the 
northern  hemisphere,  from  the  equator  to  the  pole.  The 
arrows  show  the  direction  of  the  aerial  currents.  The 
warm  air  from  the  tropics,  ascending  to  a  certain  height  in 
the  atmosphere,  flows  northward  as  an  upper  current;  on 
cooling  down  it  descends  about  the  30th  parallel  of  lati- 
tude, and  blows  as  a  south-west  wind  between  that 
parallel  and  the  60th ;  getting  warm  by  contact  with  the 
earth's  surface,  it  again  ascends,  still  flowing  towards  the 
pole,  where  it  at  length  precipitates  itself  and  forms  the 
polar  gales.  Returning  now  southwards,  it  ascends  at  the 
60th  parallel,  blowing  as  an  upper  current,  till,  on  getting 
chilled,  it  descends  at  the  30th  parallel,  and,  between  that 
and  the  equator,  blows  as  a  north-east  wind.  Thus  a 
continuous  circulation  of  air  goes  on. 

It  must  be  understood,  however,  that  these  aerial 
currents  are  subject  to  considerable  variation,  swayed  as 
they  are  by  a  number  of  disturbing  influences,  which, 
more  or  less  affect  them. 

103.   Trade  Winds— Land  and  Sea  Breezes. — The 


TKADE   WINDS.  /  :  '•:  \    V     99 


trade  winds,  so  named  from  their  imperial^  t5  J 
tion,  and  hence  to  the  purposes  of  trade,  are  those  wnich 
prevail  in  the  tropics.  They  blow  in  the  northern  hemi- 
sphere from  the  north-east,  and  in  the  southern  hemi- 
sphere from  the  south-east.  They  are  easily  accounted 
for.  In  consequence  of  the  high  temperature  of  the 
tropics,  there  is  a  continual  uplifting  of  heated  air  from 
that  region,  whilst  the  colder  air  from  the  temperate 
zones  rushes  in  to  supply  its  place.  Now,  were  the  earth 
stationary  on  her  axis,  this  colder  air  would  come  directly 
from  the  north  and  south  ;  that  is,  there  would  be  a 
north  wind  in  the  northern  hemisphere  and  a  south  wind 
in  the  southern.  But  the  earth  is  in  a  state  of  constant 
revolution  from  west  to  east,  and  from  her  configuration 
it  is  clear  that  the  different  points  in  her  surface  have 
very  different  rates  of  motion.  The  colder  air,  therefore, 
in  its  passage  towards  the  equator,  will  move  over  lati- 
tudes which  are  gradually  increasing  in  velocity.  It 
cannot  acquire  all  at  once  the  velocity  of  that  part  of  the 
earth  over  which  it  is  advancing.  It  must  necessarily 
lag  behind,  and  be  struck  by  the  objects  in  that  zone  with 
a  certain  force.  Thus  it  is  that  air  is  influenced  by  two 
motions  ;  first,  a  northerly  or  southerly  motion,  caused 
by  its  tendency  to  rush  to  the  equator  to  supply  the 
place  of  the  heated  air  there;  and  second,  an  easterly 
motion,  caused  by  the  rotation  of  the  earth. 

By  a  well-known  principle  in  dynamics  *  the  air  will 
obey  neither  the  one  motion  nor  the  other,  but  will  take 
an  intermediate  course.  In  other  words,  the  wind  will 
blow  from  the  north-east  in  the  one  case,  and  south-east 
in  the  other. 

The   following   familiar    illustration    may   be    given  : 

*  The  principle  here  referred  to  is  the  "parallelogram  of 
motion."  If  a  point  A  is  urged  by  a  force  which  would  make  it 
move  over  the  space  A  B  in  a  certain  time,  and  by  another  force 
over  A  C  in  the  same  time,  then  completing  the  parallelogram, 
the  point  under  the  influence  of  the  two  forces  will  move  through 
the  diagonal  A  D. 


100  HEAT. 


la  horseman  to  gallop  along  towards  tlie  east  on 
•si  quiet  day;  his"  motion  will  give  rise  to  a  certain  resist- 
ance on  the  part  of  the  air,  and  he  will  imagine  that  an 
east  wind  is  blowing  ;  but  let  him  do  the  same  thing 
when  a  slight  north  or  south  wind  is  blowing,  his  motion 
will  give  an  easterly  character  to  either  wind,  and  he 
will  judge  of  the  wind  as  coming  from  the  north-east  or 
south-east.  There  is  a  similar  effect  in  the  trade  winds. 

The  land  and  sea  breezes  are  peculiar  to  maritime  local- 
ities. During  the  night  the  land  loses  its  heat  by  radiation 
more  rapidly  than  the  sea,  the  cool  air  from  the  land 
therefore  makes  its  way  to  the  sea,  displacing  the  warmer 
air  there.  This  constitutes  the  land  breeze.  During  the 
day  the  reverse  takes  place;  the  cool  air  from  the  sea 
flows  to  the  land,  forming  the  sea  breeze.  The  beneficial 
effects  of  the  sea  breeze  are  particularly  felt  in  tropical 
climates.  Many  islands  would  be  almost  uninhabitable 
were  it  not  for  the  sanitary  influence  of  this  breeze. 


CHAPTER  IV. 

104.  Aqueous  Vapour  —  Evaporation. — The  atmo- 
sphere, however  clear  and  pure  it  may  appear,  always 
contains  a  quantity  of  watery  vapour,  existing  as  an  im- 
palpable transparent  gas.  The  amount  varies  in  different 
portions  of  the  atmosphere,  but  is  generally  small.  Thus, 
in  100  parts  of  ordinary  air  there  are  found  to  be  only 
•45  parts  of  aqueous  vapour,  the  remaining  99-55  parts 
consisting  of  the  other  constituents,  oxygen,  nitrogen, 
and  carbonic  acid  gases.  How  does  this  aqueous  vapour 
originate  ?  By  the  slow  and  mysterious  process  of  evap- 
oration. 

That  this  process  is  in  constant  action  is  proved 
from  various  familiar  facts.  A  tumbler  of  water  put 
outside  a  window  in  dry  weather  gradually  loses  its  con- 
tents,. ]^Q  sooner  are  our  streets  watered  than  they 


POINT    OF 


SATURATION.  ',        h  \   \  \      101 


begin  to  dry.  Wet  clothes,  in  like  mamieiS;  hurig  Ujfroli. 
an  open  place  soon  lose  their  moist urd '* 'The  J rate' aft 
which  evaporation  takes  place  depends  upon  the  temper- 
ature of  the  air.  Even  at  a  low  temperature  we  find 
evaporation  still  going  on.  A  piece  of  ice,  for  example, 
when,  exposed  to  severe  cold,  gradually  diminishes  in  size, 
and  eventually  disappears.  On  the  other  hand,  as  th° 
temperature  is  increased,  evaporation  takes  place  more 
readily.  Hence  the  rapidity  with  which  our  streets  are 
dried  in  summer  after  a  shower  of  rain.  Hence  also  the 
diminished  size  of  our  rivers  in  summer  after  a  continu- 
ance of  fine  weather. 

105.  Point  of  Saturation. — It  can  readily  be  imagined, 
therefore,  that  even  throughout  the  same  day  evaporation 
will  take  place  at  different  rates,  resulting  from  the 
varying  heating  power  of  the  sun,  and  therefore  that  the 
quantity  of  aqueous  vapour  carried  up  will  also  vary. 
Thus,  though  there  be  considerable  difference  in  the 
capability  of  the  air  as  regards  the  suspension  of  aqueous 
vapour  for  different  temperatures,  there  is  for  each 
temperature  a  definite  quantity  which  can  be  elevated. 
When  air  has  reached  this  state  it  is  said  to  be 
saturated,  or  to  have  attained  its  point  of  saturation. 
Thus,  if  there  are  two  equal  masses  of  air,  of  40°F.  and 
70°R  respectively,  each  can  take  up  its  own  definite 
quantity  of  vapour;  but  the  former,  owing  to  its  lower 
temperature,  Avill  reach  its  point  of  saturation  sooner 
than  the  latter. 

108.  Air  Heated  by  Compression  and  Chilled  by 
Expansion. — When  air  is  compressed  heat  is  evolved. 
This  can  be  shown  by  taking  a  brass  cylinder  with  a 
piston  fitting  it  air-tight  (fig.  80).  In  a  small  aperture 
at  the  end  of  the  piston-rod  is  inserted  a  piece  of  tinder. 
If  now  the  piston  be  forced  down  into  the  cylinder,  the 
air  inside  becomes  compressed,  and  sufficient  heat  is 
evolved  to  kindle  the  tinder. 

An  instrument  of  this  kind  has  been  long  in  use 
among  some  of  the  native  tribes  of  India. 


102 


HEAT. 


air  is  rarefied  or  expanded  cold  is  pro- 
'.A  striking  proof  of  this  is  afforded  when  a 
receiver  is  being   exhausted  by 
an  ail-  pump.     After  one  or  two 
strokes   a   cloudy  appearance   is      _ 
observed  in  the  receiver,  result- 
ing from  the  condensation  of  the    _. 
suspended  vapour  in  consequence! 
of  the  air  being  chilled. 

107.  Clouds  — Bain.—  If  aj 
heated  mass  of  air,  charged  with' — *• 
aqueous  vapour,  be  carried  aloft, 
it  will  expand  by  reason  of  the 
diminished  pressure  upon  it,  and 
become  chilled.  It  can  no 
longer,  therefore,  hold  all  its 
vapour  in  suspension  ;  condensa- 
tion sets  in,  and  that  the  more 
rapidly  as  it  ascends,  hence  the 
formation  of  a  cloud.  Cl 
therefore,  are  masses  of  aqu 
vapour  in  a  partially  conden 
state.  They  are  not  so  high  as 
they  appear.  The  greater  number 
of  clouds  we  see  are  within  a 
few  thousand  feet  of  the  earth's 
surface.  Hence  a  mountain 
traveller  often  becomes  enveloped 
in  clouds,  or  if  he  has  attained 
a  considerable  elevation,  he  may 
witness  some  clouds  floating  be- 
low him.  The  motion  of  clouds  is  not  so  regular  as  we 
are  apt  to  suppose;  they  have  not  a  motion  of  trans- 
ference merely,  but  also  one  in  a  vertical  direction, 
arising  from  the  continued  and  variable  effects  of  ascend- 
ing currents. 

If  the  condensation  of  the  vapour  in  the  atmosphere 
be  not  confined  to  the  higher  regions,  but  is  spread  over 


DEW.  103 

the  surface  of  the  earth,  then  there  is  a  mist  or  fog 
formed.  Fogs  arise,  for  the  most  part,  from  the  surfaces 
of  rivers,  or  lakes,  or  from  the  damp  ground  being  warmer 
than  the  superincumbent  air. 

Rain  is  caused  by  a  considerable  diminution  in  tempera- 
ture, and  therefore  by  a  rapid  condensation  of  the  aqueous 
vapour.  A  cloud  is  capable  of  holding  its  moisture  so  long 
as  the  temperature  keeps  sufficiently  high,  but  should  it 
be  carried  by  the  wind  into  a  cool  region,  it  becomes  no 
longer  able  to  do  so ;  rapid  condensation  sets  in,  vesicle 
unites  with  vesicle,  and  rain  falls.  At  first  the  drops  are 
small,  but  they  gradually  increase  in  size,  from  their 
uniting  with  other  vesicles  in  their  descent.  The  rapidity 
of  the  rain-fall  depends  upon  the  amount  of  vapour  in  the 
cloud,  and  upon  the  decrease  of  temperature  to  which 
it  is  subjected.  If  these  elements  are  carried  out  far, 
then  the  rain-fall  will  be  correspondingly  great,  hence 
the  heavy  rains  in  thunderstorms. 

108.  Dew — Dew-point— Hoar-frost. — The  phenome- 
non of  dew  affords  a  vivid  demonstration  of  the  con- 
stant presence  of  aqueous  vapour  in  the  atmosphere. 
It  is  easy  of  explanation.  After  sunset,  the  different 
objects  on  the  earth's  surface  begin  to  radiate  or  part 
with  the  heat  which  they  have  absorbed  during  the 
day ;  as  the  night  advances  this  radiation  proceeds, 
until  at  length  they  acquire  a  much  lower  temperature 
than  the  air  above  them.  The  consequence  is  that  the 
air  gets  chilled  below  the  point  at  which  it  can  hold 
its  vapour  in  suspension,  condensation  ensues,  and  a 
deposition  of  moisture  or  dew  takes  place.  The  point  at 
which  the  deposition  begins  is  termed  the  dew-point.  The 
amount  of  this  deposition  on  the  different  objects  depends 
upon  their  radiating  powers.  Thus,  dew  is  found  to  form 
copiously  on  grass,  the  leaves  of  flowers  or  trees,  and  on 
other  products  of  vegetation,  because  these  are  good 
radiators  of  heat ;  whilst,  again,  the  supply  is  small  on 
stones  or  the  naked  soil,  because  their  radiating  power  is 
feeble. 


104  HEAT. 

It  is  only,  however,  in  certain  states  of  the  atmosphere 
that  dew  is  deposited.  Cloudy  or  windy  nights  are  un- 
favourable to  its  production.  In  the  former  case,  though 
there  is  radiation  going  on  from  the  earth's  surface,  yet 
the  clouds  are  also  good  radiators,  and  they  thus  prevent 
the  surface  from  being  cooled  much  below  the  temperature 
of  the  atmosphere ;  in  the  latter  case,  the  constant  trans- 
fer of  the  air  from  place  to  place  acts  as  a  preventive. 
Clear  still  nights,  on  the  other  hand,  are  the  most 
favourable,  for  then  the  radiation  goes  on  freely. 

Hoar-frost  is  just  dew  in  a  frozen  state.  The  formation 
of  hoar-frost  is  therefore  entirely  influenced  by  the  causes 
affecting  the  deposition  of  dew. 

109.  Snow — Snow-Crystals. — When  the  temperature 
of  the  air  is  below  32°F.,  the  vesicles  of  vapour  become 
frozen,  and  in  uniting  together  become  heavier  than  the 
air,  and  fall  as  snow.  The  flakes  are  sometimes  small,  at 
other  times  large,  their  size  depending  upon  the  amount 


Fig.  81. 

of  moisture  and  the  extent  to  which  the  low  temperature 
prevails.  Should  the  flakes,  on  their  descent,  encounter 
warm  strata  of  air,  a  partial  fusion  takes  place,  and  they 
fall  in  a  half-melted  state,  forming  sleet. 

Examined  with  the  microscope,  snow  presents  a  very 


SPECIFIC   HEAT.  105 

beautiful  appearance ;  it  is  formed  of  a  number  of  dis- 
tinct and  transparent  crystals  of  ice,  which  are  observed 
to  be  grouped  together  in  a  variety  of  ways.  .Fig.  81 
exhibits  some  of  the  different  forms  of  snow-crystals 
which  are  found. 

110.  Hail. — Hail  may  be  regarded  as  frozen  drops  of 
rain.  A  small  hard  nucleus,  or  centre,  is  first  formed  in 
the  upper  regions  of  the  atmosphere ;  this,  on  its  descent, 
collects  more  and  more  moisture  on  the  surface  and 
freezes  it,  till  it  at  length  falls,  of  some  magnitude.  Hail 
rarely  falls  in  winter,  chiefly  in  spring  and  summer.  In 
winter,  from  the  prevalence  of  a  low  temperature,  the 
vapour  is  condensed  and  frozen  before  the  particles  can 
•  unite  to  form  drops;  hence,  in  that  season,  we  have  snow 
but  not  hail.  In  spring  and  summer  we  have  often 
electric  discharges,  and  as  these  sometimes  produce  a 
very  sudden  cold  in  the  region  of  the  atmosphere  where 
they  occur,  such  discharges  are  not  unusually  accom- 
panied by  a  fall  of  hail.  Hail-storms  are  often  a  groat 
scourge  to  the  agriculturist. 


CHAPTER  V. 

111.  Specific  Heat. — The  specific  heat  or  capacity  for 
heal  of  a  body,  is  the  quantity  of  heat  necessary  to  raise  ifc 
through  a  certain  number  of  degrees,  as  compared  with 
the  quantity  required  to  raise  an  equal  weight  of  water 
through  the  same  number  of  degrees.  In.  this  country 
it  is  customary  to  express  by  unity  the  amount  of  heat 
necessary  to  raise  one  pound  of  water  1°C.,  or,  which  is 
the  same  thing,  the  amount  of  heat  which  one  pound  of 
water  gives  out  in  falling  1°C.  This  is  known  as  the 
thermal  unit.  For  example,  take  water  and  mercury.  It 
is  found  that  thirty  times  as  much  heat  is  required  to 
raise  one  pound  of  water  1°C.  as  is  required  to  raise  one 
pound  of  mercury  1°C.  If,  therefore,  we  express  the 


106 


HEAT. 


specific  heat  of  water  by  1,  we  must  express  the  specific 
heat  of  mercury  by  -^  or  -03. 

112.  Methods  of"  Measuring  the  Specific  Heat  of 
Bodies. — We  mention  two  methods  of  measuring  specific 
heat. 

(1)  Method  of  Mixtures. — This  consists  in  placing  a 
given  quantity  of  the  substance  (whose  specific  heat  is 
required)  at  a  given  temperature,  in  a  given  quantity  of 
water  at  a  lower  temperature,  and  ascertaining  the  loss 
of  heat  by  the  former,  and  the  gain  by  the  latter.  An 
example  will  illustrate  the  method  :  Suppose  we  mix 
5  Ibs.  of  a  fluid  (call  it  A)  at  80°C.,  with  2  Ibs.  of  water 
at  10°C.,  and  that  the  temperature  of  the  mixture  is  25°C.; 
denote  by  x  the  specific  heat  of  the  fluid.  We  have  here 
a  decrease  of  temperature  in  A  of  55°,  and  an  increase 
in  the  water  of  15°.  Therefore  the  amount  of  heat  given 
out  by  5  Ibs.  of  A  will  be  expressed  by  5  x  55  x  x'}  whilst 
the  amount  of  heat  absorbed  by  the  2  Ibs.  of  water  will 
be  expressed  by  2  x  15  x  1.  Then,  since  the  loss  of  heat 
in  the  one  case  is  just  equal  to  the  gain  in  the  other,  we 
have  5  x  55  x  x  =  2  x  15,  and  x  =  f£J|  =  -109  nearly,  hence 
the  specific Jieat  of  A=  '109. 

(2)  The  Ice  Calorimeter. — This 
instrument  was  invented  by  the 
French  philosophers,  Lavoisier 
and  Laplace.  A  sectional  draw- 
ing of  it  is  shown  in  fig.  82. 
It  consists  of  three  tin  vessels, 
one  within  the  other,  the  spaces 
A,  B,  between  being  filled  up 
with  pounded  ice  at  0-0°.  The 
body,  whose  specific  heat  is  to 
be  determined,  is  placed  in  the 
central  one.  There  are  two 
stop  cocks  E,  D,  for  running 
off  the  water  caiised  by  the 
Fig.  82.  fusion  of  the  ice  on  the  part 

of  the  surrounding   atmosphere   and   the   heated   body 


TABLE   OP   SPECIFIC   HEATS.  107 

respectively.  In  order  to  use  it,  the  body  of  weight 
"W,  suppose,  being  raised  to  a  given  temperature  t,  is 
quickly  placed  in  the  central  vessel,  and  allowed  to  re- 
main there  till  its  temperature  sinks  to  0°C.  The  water 
resulting  from  the  fusion  of  the  ice  is  then  drawn  off  at 
the  stop  cock  D  and  weighed.  Let  this  weight  be  w. 
Now,  as  it  requires  80°C.  of  heat  to  convert  a  pound  of 
ice  at  0°C.  into  water  at  0°C.  (see  Art.  117),  the  quantity 
of  heat  absorbed  by  the  collected  water  will  be  expressed 
by  80  x  w;  whilst  the  quantity  of  heat  given  out  by  the 
body  will  be  expressed  by  W  x  t  x  x,  where  x,  as  before, 
is  the  specific  heat  required.  "We  have  therefore  the 

equation,  W  xtxx--=8Qw;  hence  x  =  =yyr~^' 

A  certain  amount  of  error  results  in  the  use  of  this  in- 
strument, from  the  fact  that  all  the  water  does  not  escape; 
part  of  it  adheres  to  the  ice  in  its  half-melted  state. 

113.  Table  of  Specific  Heats.  — The  following  table 
gives  the  specific  heats  of  certain  bodies  : — 

MEAN  OF  SPECIFIC  HEATS  BETWEEN  0°C.  AND  100°  C. 

Water I'OOOO  Iron 1138 

Alcohol -4534  Copper $951 

Mercury '0333  Lead '0314 

The  above  table  gives  the  mean  or  average  specific  heats 
between  0°  and  100°.  It  has  been  found  that  the  specific 
heat  of  bodies  increases  with  the  temperature,  and  more 
so  in  liquids  than  in  solids.  In  the  case  of  water,  how- 
ever, this  increase  is  less  than  in  solids. 

114.  Experimental  Illustration. — The  difference  which 
subsists  between  bodies,  in  regard  to  their  capacity  for 
heat,  may  be  strikingly  shown  by  the  following  experi- 
ment : — A  cake  of  bees'- wax  is  placed  upon  the  ring  of  a 
chemical  stand  (fig.  83).     Three  balls  of  different  metals — 
iron,  copper,  lead,  are  immersed  in  a  bath  of  very  hot 
oil  till  they  all  acquire  its  temperature.     If  now  they  be 
taken  out  and  put  upon  the  cake,  they  make  their  way 


108 


HEAT. 


through  at  different  rates — the  iron  ball  first,  the  copper 

,iiext,  and  last  of  all  the  lead. 
115.  Influence  of  the  High 
Specific  Heat  of  Water  on 
Climate. — The  high  specific 
heat  of  water  plays  an  im- 
portant part  in  the  economy 
of  nature.  The  specific  heat 
of  air  has  been  found  to  be 
nearly  4 '2  times  less  than  that 
of  water.  It  follows  therefore 
that  1  Ib.  of  water  in  losing 
1°C.,  Avould  warm  4 '2  Ibs  of 
fc^  air  1°C.  But  water  is  770 
times  as  heavy  as  air;  hence, 
comparing  equal  volumes,  a 
£•  83>  cubic  foot  of  water  in  losing 

1?C.,  would  raise  770  x  4-2,  or  3234  cubic  feet  of  air 
1^0.  We  see  from  this,  "the  great  influence  which  the 
ocean  must  exert  on  the  climate  of  a  country.  The  heat 
of  summer  is  stored  up  in  the  ocean,  and  slowly  given 
out  during  the  winter.  Hence  one  cause  of  the  absence 
of  extremes  in  an  island  climate."* 

116.  Latent  Heat. — During  the  passage  of  a  body  from 
the  solid  to  the  liquid  stats,  or  from  the  liquid  to  the 
gaseous  state,  its  temperature  remains  constant,  whatever 
be  the  intensity  of  the  heating  source.  The  heat  which 
the  body  receives  in  its  transition  state,  does  not  affect 
the  thermometer,  does  not  manifest  itself,  and  on  this 
account  it  is  called  "  latent."  We  may  define  latent  heat, 
therefore,  as  the  quantity  of  heat  which  disappears  or  is 
lost  to  thermometric  measurement,  when  the  molecular  con- 
stitution of  a  body  is  being  changed. 

Thus  if  we  take  a  block  of  ice,  say  at  -  10°  C.,  and  apply 

heat  to  it,  its  temperature  rises  till  it  comes  up  to  0°C. 

At  this  point  the  temperature  remains  stationary  until 

the  last  particle  of  ice  is  melted.     When  this  takes  place, 

*  Tyndall  on  Heat  as  a  Mode  of  Motion)  p.  143. 


LATENT   HEAT   OF   WATER   AND   STEAM.  109 

the  temperature  again  rises  till  it  reaches  100°C.,  when 
it  once  more  remains  stationary,  the  water  then  gradually 
passing  off  in  the  form  of  steam. 

117.  Latent  Heat  of  Water  and  Steam— (1)  Water.— 
If  1  lb.  of  water  at  80°  C.  be  mixed  with  1  Ib.  of  water 
at  0°,  the  temperature  of  the  mixture  is  40°  C.  But  if 
1  lb.  of  water  at  80°  C.  be  mixed  with  1  lb.  of  pounded 
ice  at  0°,  there  will  result  2  Ibs.  of  water  at  0°C.  It 
follows  therefore  that  1  lb.  of  ice  at  0°  C.,  in  being  changed 
into  1  lb.  of  water  at  0°d,  requires  as  much  heat  as 
would  raise  1  lb.  of  water  through  80° C.,  or,  which  is  the 
same  thing,  as  would  raise  80  Ibs.  of  water  1°C.  Con- 
sequently the  number  80°C.  (144°F.)  expresses  the  latent 
heat  of  water  or  of  the  fusion  of  ice. 

(2)  Steam. — The  latent  heat  of  steam  may  be  deter- 
mined by  observing  the  time  required  to  raise  a  given 
quantity  of  water  through  a  certain  number  of  degrees, 
and  then  comparing  this  with  the  time  between  the  com- 
mencement of  boiling  and  the  total  evaporation  of  the 
water.  It  has  been  estimated  at  540°C.,  implying  that 
during  the  conversion  of  1  lb.  of  water  at  100*0.  into 
1  lb.  of  steam  at  the  same  temperature,  as  much  heat  is 
imparted  as  would  raise  540  Ibs.  of  water  1°C. 

The  latent  heat  of  steam  is  of  service  in  cookery. 
Vegetables  and  meat  are  often  cooked  by  allowing  the 
steam  from  boiling  water  to  pass  through  them;  in  doing 
so,  the  steam  becomes  condensed  and  parts  with  its  latent 
heat.  "We  can  easily  understand  from  this  the  severity  of 
a  scald  from  steam. 

Solution  of  Questions. — The  student  would  do  well 
to  note  the  following  questions,  and  the  method  of  solving 
them : — 

Ex.  1. — How  many  pounds  of  ice  at  0°C.  can  be  melted 
by  1  lb.  of  steam  at  100°  C.  ? 

Let  x  be  the  number.  Then  since  1  lb.  of  ice  re- 
quires 80  units  of  heat  to  convert  it  into  ivater,  x  Ibs. 
will  require  80  x  x.  Again,  1  lb.  of  steam  at 
JOO°C.,  in  being  converted  into  water  at  100°C., 


110  HEAT. 

gives  out  540  units  of  heat,  and  the  1  Ib.  of  ivater 
has  further  to  give  out  100  tmits;  hence  the  whole 
heat  given  out  by  the  steam  when  reduced  to  water 
at  0°C.  =  540+ 100.  But  this  heat  is  absorbed 
by  the  ice,  therefore  we  have  80  x  x  =  540  +  100, 
and  x  =  S  Ibs. — Ans. 

Ex.  2. — How  many  pounds  of  steam  at  100°C.  ivilljust 
melt  100  Ibs.  of  ice  at  0°C.  ? 

If  x  be  the  number,  then  the  quantity  of  heat 
given  out  by  x  Ibs.  of  steam  at  100°,  when  reduced 
to  water  at  0°  =  540#+100ce;  whilst  the  quantity 
of  heat  required  by  the  100  Ibs.  of  ice  to  convert 
it  into  water  at  0°  =  100  x  80;  hence  540  x  +  100  x 
=  100  x  80,  and  x  =  12J. — Ans. 

Ex.  3. — What  weight  of  steam  at  100°C.  would  be 
required  to  raise  500  Ibs.  of  water  from  0°C.  to 
10°C.  ? 

Let  x  be  the  number  of  pounds.  Here  the  quan- 
tity of  heat  given  out  =  540  x  +  90  x  (the  water  at 
100Q  C.  is  to  sink  to  10°  C.) ;  hence  540  x  +  90  x  = 
500  x  10,  and  x  =  7'9  Ibs. — Ans. 

Ex.  4. — If  4  Ibs.  of  steam  at  100°C.  be  mixed  with 
200  /6s.  of  water  at  10°C.,  what  will  be  the  tem- 
perature of  the  water  ? 

Let  x  be  the  temperature.      4  Ibs.  of  steam  in 

becoming   water  give   out   a  quantity  of  heat  = 

4  x  540,  and  produce  4  Ibs.  of  water  at  100°; 

further,  the  4  Ibs.  of  water  have  to  give  out  the 

additional  heat  4  (100- a).     Again,  the  200  Ibs. 

of  water  in  rising  from  10  to  x,  absorb  a  quantity 

of  heat  =  200  (x  -  10);  hence  4  x  540  +  4  (100  -  x) 

-200  (a -10),  and  x  =  22° -3.—  Ans. 

118.  Cold  Of  Evaporation, — In  the  passage  of  water 

or  any  other  liquid  into  vapour,  there  is  a  quantity  of 

heat  rendered  latent.     This  heat  is  chiefly  derived  from 

the  liquid  itself,  hence  the  temperature  of  the  liquid  is 

lowered.     We  have  therefore  the  important  fact  that  cold 

is  produced  by  evaporation.     The  more  rapidly  evapora- 


FREEZING  BY   EVAPORATION.  Ill 

tion  proceeds,  the  degree  of  cold  is  the  greater.  If,  for 
example,  we  take  the  three  liquids,  water,  alcohol,  and 
sulphuric  ether,  and  place  a  drop  of  each  successively  on 
the  hand,  then  waving  the  hand  backwards  and  forwards 
in  the  air  to  hasten  the  evaporation,  we  find  that  the 
sensation  of  cold  is  least  with  the  water,  greater  with  the 
alcohol,  and  still  greater  with  the  ether.  This  arises  from 
the  rate  of  evaporation  at  the  same  temperature  being 
different  in  the  three  liquids. 

119.  Freezing  by  Evaporation.  —  Evaporation  may 
proceed  so  rapidly  as  to  cause  refrigeration.  This  may 
be  effected  in  the  following  manner :— A  small  capsule 


Fig.  84. 

containing  water  is  placed  in  a  flat  dish  filled  with  sul- 
phuric acid.  The  whole  is  placed  under  the  receiver  of 
an  air-pump,  and  the  air  exhausted.  As  the  rarefaction 
proceeds  the  water  evaporates,  the  vapour  being  imme- 


112  HEAT. 

diately  absorbed  by  the  sulphuric  acid,  till  the  remaining 
water  begins  to  freeze,  and  eventually  becomes  a  solid 
lump.  This  experiment  is  due  to  Leslie. 

Another  experiment  consists  in  filling  a  test  tube  with 
water,  surrounding  it  with  cotton  wool  saturated  with 
sulphuric  ether,  and  blowing  a  stream  of  air  upon  it  by 
means  of  a  pair  of  bellows  (fig.  82).  The  evaporation 
of  the  ether  takes  place  rapidly,  and  the  water  in  a 
short  time  becomes  frozen. 

The  method  often  followed  out  in  India  of  procur- 
ing ice,  affords  an  illustration  of  the  same  thing. 

Early  in  the  cold  weather,  when  the  nights  are  clear, 
shallow  unglazed  earthenware  pans  filled  with  water  are 
put  out  in  the  open  air.  Evaporation  rapidly  takes 
place,  and  during  the  process,  when  the  temperature 
falls  below  the  freezing  point,  a  thin  stratum  of  ice 
forms  on  the  surface  of  the  water.  Before  daybreak 
the  thiii  cakes  of  ice  are  removed  from  the  pans,  and 
the  accumulated  mass,  well  hammered  together,  is  stowed 
away  in  the  ice-house. 

Water  coolers,  so  much  used  in  summer,  owe  their 
action  to  the  same  principle. 


Fig.  85. 

A  remarkable  instance  of  freezing  by  evaporation  occurs 
in  a  grotto  near  Yergy  in  France.  In  some  places  columns 
of  ice  appear  to  support  the  vault  of  the  grotto ;  at  others 
they  are  seen  hanging  from  the  roof,  or  resting  upon  t^e 


CONDUCTION   OF   HEAT.  113 

ground.  The  water  passes  slowly  in  traversing  the 
vault,  and  its  evaporation  hastened  by  currents  of  air 
produces  the  ice.  It  is  not  in  winter  alone  that  this 
takes  place,  nor  can  the  formation  of  the  "  glacier es 
naturelles"  be  attributed  to  a  cooling  down  of  the  air. 

120.  The  Cryophorus. — This  instrument,  invented  by 
Wollaston,  is  founded  on  the  same  principle.  It  is  repre- 
sented in  fig.  85.  It  consists  of  two  glass  bulbs,  A  and 
B,  connected  by  a  tube.  Water  is  put  in  the  bulb  A,  and 
whilst  a  small  orifice  is  left  open  at  the  bottom  of  the  bulb 
B,  the  water  is  boiled ;  the  steam  escaping  from  the  water 
chases  out  the  air,  and  when  this  is  all  expelled,  the  orifice 
is  closed  by  means  of  a  blowpipe.  On  the  water  regaining 
its  ordinary  temperature,  there  is  left  in  the  apparatus 
nothing  but  a  little  water  and  its  vapour.  If  now  the 
bulb  A  be  placed  in  a  vessel  to  get  rid  of  currents  of  air, 
whilst  the  other  bulb  B  is  plunged  into  a  freezing  mix- 
ture, such  as  snow  and  salt,  the  vapour  as  it  escapes 
from  the  water  is  condensed,  and  in  the  course  of  half 
an  hour  or  so  the  water  in  A  begins  to  freeze. 


CHAPTER  VI. 

121.  Convection  of  Heat, — By  the  convection  of  heat 
is  meant  that  process  by  which  heat  is  carried  and  dis- 
tributed through  the  mass  of  a  fluid  body  by  the  actual 
motion  of  its  own  particles.  Thus,  water  is  boiled  by  con- 
vection.    When  heat  is  applied  to  a  vessel  of  water,  as  in 
iig.  86,  there  are  produced  a  series  of  ascending  currents 
which  carry  the  heat  to  the  other  parts  of  the  liquid, 
until  the  water  is  raised  to  the  boiling  point.     In  like 
manner,  the  air  at  the  top  of  a  room  is  heated  by  the 
ascending  currents  of  warm  air.      The    phenomena  of 
winds  are  due  also  to  convection. 

122.  Conduction  of  Heat. — Heat  is  said  to  be  con- 
ducted   when    it    is    propagated    along    the    yiolecules 

8  E  H 


1H 


HEAT. 


of  a,  body.  There  is  a  great  difference  between  bodies 
in  regard  to  their  conducting  power,  or  conductivity, 
as  it  is  more  generally  called.  Thus,  if  a  rod  of  iron  and 
a  rod  of  wood  of  the  same 
length  and  diameter  be  taken, 
and  an  end  of  each  be  inserted 
in  the  fire,  in  a  short  time 
the  other  end  of  the  iron  rod 
will  become  heated,  whilst  no 
trace  of  heat  will  yet  appear 
at  the  other  end  of  the  wooden 
rod.  In  such  an  experiment, 
therefore,  it  is  clear  that  the 
heat  has  found  a  ready  passage 
through  the  iron  rod,  and  has 
met  with  considerable  resist- 
ance in  the  wooden  rod. 
Hence  we  may  divide  bodies, 
considered  in  relation  to  their 
conductivity,  into  two  classes  : 
good  and  bad  conductors. 
Under  the  former  class  may 
Fig.  86.  be  included  the  metals,  and 

under  the  latter  such  bodies  as  wood,  stone,  glass,  straw, 
wool,  cotton,  silk,  etc. 

All  liquids  and  gases  possess  a  very  feeble  conducting 
power.  If,  for  example,  a  vessel  of  water  be  heated  from 
tlie  top  by  pouring  gently  on  the  surface  a  quantity  of 
boiling  oil,  it  is  found  that  the  heat  makes  its  way 
downwards  with  extreme  slowness,  and  it  is  only  after 
a  considerable  time  that  the  least  rise  in  temperature  is 
observable  at  the  bottom  of  the  vessel. 

Snow  is  a  very  imperfect  conductor  of  heat.  Travel- 
lers, when  overtaken  by  a  snow-storm,  in  some  instances 
have  had  their  lives  preserved  by  taking  shelter  in  a 
wreath  of  snow,  before  being  benumbed  by  the  cold.  So 
also  sheep  have  been  taken  out  alive,  though  buried 
amidst  snow  for  some  time. 


RELATIVE  CONDUCTIVITY   OP   BODIES. 


115 


The  Esquimaux,  it  is  said,  construct  their  winter  huts 
of  snow.  They  shape  the  snow  into  large  hard  masses, 
which  they  place  upon  each  other  as  our  masons  do 
stones ;  they  then  pour  into  the  crevices  ice-cold  water, 
which  upon  freezing  unites  the  whole  into  one  solid  mass. 
The  inside  being  covered  with  the  skins  of  animals,  a 
comfortable  dwelling  is  thus  provided. 

This  quality  of  snow  is  not  without  its  use  in  the 
general  economy  of  nature.  In  severe  climates,  it  pre- 
vents the  earth  from  being  so  much  cooled  down  as  to 
endanger  those  germs  of  vegetation  which  await  the 
return  of  spring. 

123.  Relative  Conductivity  of  Bodies.  —  Several 
methods  have  been  followed  out  with  a  view  to  deter- 
mine the  relative  conductivity  of  different  substances. 
One  method  is  this  :  A  rectangular  bar  of  uniform  thick- 
ness (fig.  87)  is  heated  at  one  end.  A  number  of  holes 


Fig.  87. 

are  made  at  equal  distances  along  the  bar,  sufficient  to 
hold  the  bulbs  of  so  many  thermometers.  "When  the 
heating  source  is  applied,  the  thermometers  begin  to 
rise,  but  at  very  different  rates — the  one  nearest  rising 
the  fastest,  whilst  the  one  farthest  away  is  but  little 


116  HEAT. 

affected.  The  rates  at  which  the  different  thermometers 
rise  are  then  carefully  noted.  The  same  thing  is  done 
with  bars  of  different  material ;  and  by  comparing  the 
rates  of  ascent  of  one  set  of  thermometers  with  those  of 
others,  the  relative  conductivities  of  the  substances  are 
ascertained. 

The  following  table  has  been  constructed  from  such  in- 
vestigations : — 

Name  of  Substance.  Conductivity. 

Silver, 100 

Copper, 74 

Gold, 53 

Iron, 12 

Lead, 9 

Platinum, 8 

Bismuth, 2 

It  is  interesting  to  note  the  fact  that  the  numbers  con- 
tained in  the  above  table  nearly  express  the  conductive 
powers  of  the  bodies  for  electricity. 

124.  Experimental  Illustration.  —  The  difference  in 
the  conductivity  of  metals  may  be  illustrated  by  the  fol- 
lowing simple  experiment. 

Two  bars  of  different  metals,  such  as  copper  and  iron, 
are  placed  as  in  fig.  88.  At  equal  distances  along  the 


Fig.  88. 

bars  are  attached  a  series  of  wooden  balls  by  means  of 
wax.  When  the  ends  are  heated  by  a  lamp,  the  heat  is 
propagated  along  the  bars,  but  as  the  copper  is  a  better 
conductor  than  the  iron,  the  wax  on  the  former  is  more 
readily  melted,  and  a  greater  number  of  balls  fall  off 
from  the  copper  than  from  the  iron  in  the  same  time. 


SENSATIONS  otf  HEAT  AND  COLD.  117 

125.  Effect  of  Mechanical  Texture. — Mechanical  tex- 
ture has  an  effect  on  the  conduction   of    heat.      Thus, 
twisted  silk  conducts  heat  more  readily  than  raw  silk; 
hard  rock  crystal  more  readily  than  when  reduced  to 
powder  ;  wood  more  readily  than  in  the  state  of  sawdust. 
The  reason  is  that  in  the  latter  cases  the  molecular  chain 
is  not  so  continuous;  it  is  broken  up  by  air-spaces. 

126.  Clothing. — As  the  object  of  clothing  is  to  prevent 
the  escape  of  heat  from  the  body,  we  must  of  course  select 
those  substances  as  articles  of  dress  which  offer  resist- 
ance to  the  passage  of  heat,  or  such  as  are  bad  conduc- 
tors.    The  common  notion  that  there  is  natural  warmth 
in  any  material  is  quite  a  wrong  one.     There  is  really  no 
more  natural  heat  in  a  piece  of  flannel  than  there  is  in 
a  piece  of  lead.     Flannel  is  an  excellent  covering  for  a 
man  in  winter;  it  is  nevertheless  also  the  best  substance 
for  -wrapping  round  ice  to  prevent  it  melting  in  summer. 
In  the  former  case  the  source  of  heat  being  within,  the 
flannel  prevents  the  escape  of  heat,  and  thus  contributes 
largely  to  warmth ;  in  the  latter  case,  the  source  of  heat 
is  from  without,  and  the  flannel  being  a  bad  conductor 
effectually  prevents  the  passage  of  heat  into  the  ice. 

There  being  therefore  no  such  thing  as  natural  warmth  in 
any  material,  it  is  evident  that  the  lower  the  temperature 
to  which  we  are  exposed,  the  greater  the  waste  of  animal 
heat  would  be ;  hence  in  cold  weather  it  becomes  neces- 
sary to  surround  the  body  with  such  materials  as  are  the 
worst  conductors  of  heat.  Now,  according  to  experiment, 
fur  is  the  worst  conductor,  and  therefore  the  warmest 
covering ;  next  to  it  is  wool,  fabricated  into  the  different 
textures  of  flannel  and  cloth ;  next  are  cotton,  linen,  and 
silk,  Avhich,  being  better  conductors,  form  therefore  a  com- 
paratively cool  covering,  and  are  fit  only  for  the  higher 
temperatures  of  summer. 

Air  is  a  bad  conductor  of  heat;  hence  loose  clothing  is 
warmer  than  we  are  apt  to  imagine. 

127.  Sensations  of  Heat  and  Cold. — The  different 
sensations  of  heat  and  cold,  which  we  continually  experi- 


118  HEAT. 

ence  in  tottMng  bodies,  arise  altogether  from  conduction. 
When  two  bodies  of  different  temperatures  are  placed  in 
contact,  the  warmer  parts  with  its  heat  to  the  colder, 
until  they  both  acquire  the  same  temperature.  There  is  a 
constant  tendency  towards  an  equilibrium  of  temperature. 
Suppose,  then,  that  a  person  in  a  room  without  a  fire 
were  to  touch  first  the  carpet,  then  the  table,  then  the 
wall,  and  lastly  the  fender,  he  would  consider  each  of 
them  colder  and  colder  in  succession.  "Why?  The  reason 
is  simply  this :  the  carpet  being  a  bad  conductor,  carries 
little  heat  off  from  the  hand ;  the  table  is  a  better  con- 
ductor, and  thus  feels  colder ;  the  wall  is  a  better  con- 
ductor still,  and  therefore  feels  still  colder ;  but  the  fender 
is  the  best  conductor  of  the  whole,  and  accordingly  it 
carries  off  the  heat  rapidly,  giving  thereby  the  most  power- 
ful sensation. 

128.  Combustion.  —  Combustion,  such  as  we  have  it 
in  our  coal,  in  our  gas  and  candle  flames,  is  due  to  the 
chemical  union  of  the  oxygen  of  the  air  with  the  sub- 
stances present  in  these. 

Coal-gas  is  a  chemical  combination  of  carbon  and 
hydrogen.  When  the  jet  of  escaping  gas  is  ignited, 
"the  oxygen  of  the  air  unites  with  the  hydrogen, 
and  sets  the  carbon  free.  Innumerable  solid  par- 
ticles of  carbon  thus  scattered  in  the  midst  of  the 
burning  hydrogen,  are  raised  to  a  state  of  intense  incan- 
descence: they  become  white  hot,  and  mainly  to  them 
the  light  of  our  lamps  is  due.  The  carbon,  however,  in 
due  time,  closes  with  the  oxygen,  and  becomes,  or  ought  to 
become,  carbonic  acid ;  but  in  passing  from  the  hydrogen, 
with  which  it  was  first  combined,  to  the  oxygen  with 
which  it  enters  into  final  union,  it  exists  for  a  time  in 
the  solid  state,  and  then  gives  us  the  splendour  of  its 
light."  Within  the  flame  there  is  a  core  of  unburnt  gas. 

"  The  combustion  of  a  candle  is  the  same  in  principle 
as  that  of  a  jet  of  gas.  On  .igniting  the  wick,  it  burns, 
melts  the  tallow  at  its  base,  the  liquid  ascends  through 
the  wick  by  capillary  attraction,  it  is  converted  by  the 


EFFECT   OF  WIRE   GAUZE. 


119 


heat  into  vapour,  and  this  vapour  is  a  hydro-carbon, 
which  burns  exactly  like  the  gas."  * 

129.  Structure  of  a  Candle  Flame. — It  is  to  Sir 
Humphry  Davy  that  we  owe  our  knowledge  of  the  pre- 
cise theoiy  and  constitution  of  flame.  The  structure  of 
a  candle  flame  will  be  understood  from  fig.  89.  It  con- 
sists of  three  parts :  (1)  the  space 
occupied  by  the  unburnt  vapour ;  (2) 
the  luminous  zone  or  area  where  the 
carbon  particles  are  in  a  white-hot, 
glowing  state;  (3)  the  area  of  com- 
plete combustion,  from  which  the 
greatest  amount  of  heat  is  evolved. 
The  presence  of  unburnt  vapour  with- 
in may  be  shown  by  placing  a  small 
glass  tube,  as  in  the  figure.  The  va- 
pour escapes  through  the  tube,  and 
may  be  ignited  at  the  other  end. 

The  same  thing  may  be  shown  by 
lowering  a  piece  of  white  paper  upon 
the  flame  till  it  nearly  touches  the  Fig-  89. 

wick.     A  blackened  or  charred  ring  is  formed  upon 
paper,  whilst  within  the  ring  the  paper  is  unaffected. 


Fig.  90. 

130.  Effect  of  Wire  Gauze.— If  a  piece  of  fine  wire 
*     Tyndall  on  Heat  as  a  Mode  of  Motion,  pp.  46,  47. 


120 

gauze  be  lowered  upon  a  gas  jet  the  flame  spreads  out 
below  (fig.  90),  but  is  unable  to  penetrate  the  meshes  of 
the  gauze.  This  is  owing  to  the  conduction  of  the  heat 
by  the  gauze,  in  consequence  of  which  the  gas  that  escapes 
through  cannot  become  ignited.  If,  whilst  the  gas  is 
escaping,  the  gauze  be  held  a  little  above  the  burner,  it 
may  be  ignited  from  above,  but  the  flame  cannot  reach 
the  gas  below;  and  it  may  be  extinguished  by  raising  the 
gauze  quickly  upwards. 

On  this  principle  is  constructed  the    "Davy  Safety 
Lamp,"  so  much  used  by  miners. 

131.  Bunsen  Lamp. — The  luminosity  of  flames,  as  we 
have  seen,  is  mainly  due  to  the  existence  of  solid  carbon 
particles.  Hence  when  a  large  quantity  of  air  is  allowed 
to  mix  with  them  their  combustion  is  quickened,  and  heat 
is  developed  at  the  expense  of  intensity  of  light.  This  is 
what  is  effected  by  a  Bunsen  lamp,  so  much  used  in 
chemical  and  physical  laboratories.  It  is  represented  in 
fig.  91.  The  gas,  escaping  from  a  cen- 
tral burner,  up  the  tube,  draws  with  it  a 
quantity  of  air  through  the  small  holes 
near  the  base.  The  mixture  of  gas  and 
air  is  then  ignited  at  the  top  of  the 
tube,  and  burns  with  a  feeble  light,  but 
evolves  considerable  heat,  owing  to  the 
complete  combustion  of  the  carbon.  If 
the  small  holes  be  closed,  the  flame  as- 
sumes its  ordinary  appearance. 

132.  Animal  Heat.— The  heat  of  our 
bodies  is  due  to  a  slow  combustion  con- 
Fig-  91.  stantly  going  on.  The  oxygen  of  the 
air  we  inspire  combines  with  the  carbon  elements  of 
the  blood  and  animal  tissue,  and  by  their  union  heat  is 
evolved — the  carbonic  acid  thus  formed  being  constantly 
exhaled.  The  air  we  expire  contains  from  3  to  6  per  cent. 
of  carbonic  acid,  and  will  not  support  the  combustion  of 
a  candle. 


EEFLECTION  OF  RADIAN?  HEAT.         121 


CHAPTER  VII. 

133.  Radiation  of  Heat— Theory  of  Exchanges. — 
There  is  no  quality  so  abundantly  obvious  in  reference  to 
heat,  than  its  tendency  to  diffuse  itself  in  all  directions 
from  the  heating  source.     This  passage  of  heat  through 
intervening  space  is  called  radiation,  and  the  heat  thus 
passing,  radiant  heat. 

Radiation  is  not  dependent  upon  the  presence  of  air ; 
it  takes  place  also  in  a  vacuum.  This  is  manifest  when 
we  consider  how  it  is  that  we  derive  heat  from  the  sun; 
his  heating  rays  require  to  pass  through  an  intervening 
void  before  they  reach  our  earth. 

We  are  accustomed  to  speak  of  warm  bodies  only 
radiating  heat;  but  the  fact  is  that  all  bodies,  of  whatever 
temperature,  radiate  heat.  Let  us  suppose  we  have  two 
bodies,  A  and  B,  of  different  temperatures,  A  warmer 
than  B.  Radiation  takes  place  not  only  from  A  to  B,  but 
also  from  B  to  A.  However,  in  consequence  of  A's  ex- 
cess of  temperature,  more  heat  passes  from  A  to  B  than 
from  B  to  A,  and  this  continues  until  both  bodies  acquire 
the  same  temperature. 

At  this  point  the  radiation  does  not  cease ;  but  now 
the  amount  of  radiation  is  the  same  for  both — as  much 
heat  passes  from  B  to  A  as  from  A  to  B,  or  the  one 
body  gives  out  as  much  heat  as  it  receives  from  the 
other.  This  theory  is  known  as  "  Pre vest's  Theory  of 
Exchanges." 

If  we  place  ourselves  near  a  block  of  ice,  we  experience 
the  sensation  of  cold.  This  might  lead  us  to  the  belief 
that  cold  is  a  separate  influence,  and  can  be  radiated  like 
heat.  In  this  case,  however,  the  body  being  warmer 
than  the  ice,  there  is  a  greater  radiation  from  it  to- 
wards the  ice  than  from  the  ice  towards  it,  hence  the 
cause  of  the  sensation. 

134.  Reflection  of  Radiant  Heat.— Heat,  like  light, 
is  capable  of  reflection,  and  follows  the  same  law  (Art.36). 


122 


HEAT. 


The  reflection  of  heat  is  well  illustrated  by  the  apparatus 
represented  in  fig.  92.  Two  metallic  reflectors  mounted  on 
stands  are  set  directly  opposite  each  other.  A  white-hot 


Fig.  92. 

iron  ball  is  placed  in  the  principal  focus  of  one  of  the  re- 
flectors ;  if  now  a  piece  of  phosphorus  be  placed  in  the 
focus  of  the  other  reflector,  it  will  burn,  being  fired  by 
the  heat  emitted  from  the  ball,  which  has  been  concen- 
trated by  the  reflectors  at  that  point. 

The  reflective  powers  of  substances  vary  considerably. 
According  to  Leslie's  experiments,  the  greatest  reflection 
takes  place  from  bright  and  polished  metallic  surfaces. 
Should  the  surface  be  rough  or  tarnished,  the  amount 
of  reflection  is  much  diminished.  Glass  coated  with  lamp- 
black, and  white  paper,  reflect  very  feebly. 

135.  Radiating  Power  of  Bodies. — Experiment  shows 
a  marked  difference  also  in  the  powers  of  bodies  to 
radiate  heat.  A  body  which  reflects  heat  well  is  found  to 


STRANGE   EFFECT   OF   CLOSE   CONTACT.  123 

radiate  badly  ;  in  other  words,  a  good  reflector  of  heat  is 
a  bad  radiator,  and  vice  versd.  The  two  qualities,  in 
fact,  of  reflection  and  radiation,  are  directly  opposed  to 
each  other. 

In  the  interesting  researches  on  this  subject  by  Leslie, 
he  made  use  of  a  tin  canister  mounted  on  a  stand  and  filled 
with  hot  water,  the  sides  of  which  were  coated  over  with 
different  subs.tances,  e.g.,  one  with  lampblack,  a  second 
with  writing  paper,  a  third  with  glass,  and  a  fourth 
with  a  layer  of  silver.  He  found  the  radiating  powers 
of  the  faces  to  be  very  different.  Expressing  the  radia- 
tion of  lampblack  by  100,  he  found  that  of  the  paper 
to  be  98,  of  the  glass  90,  and  of  the  silvered  surface 
12.  This  apparatus  is  known  as  Leslie's  cube  or  canister. 

The  high  radiating  power  of  fire-clay  is  well  known, 
hence  the  common  expedient  of  lining  a  grate  with  this 
substance,  so  as  to  increase  the  radiation  from  the  fire. 
In  regard  to  the  metals,  it  may  be  stated  generally,  that 
the  brighter  and  more  polished  the  surface,  the  less  the 
radiation.  Of  all  substances,  lampblack  possesses  the 
highest  radiating  power. 

136.  Strange" Effect  of  Close  Contact. — Under  certain 
circumstances  the  cooling  of  a  vessel  containing  hot  water 
may  even  be  hastened  by  surrounding  it  with  flannel. 
Thus,  if  two  similar  vessels  be  taken,  both  filled  with  hot 
water — the  one  closely  enveloped  in  flannel,  and  the  other 
left  uncovered — ^he  former  is  found  to  radiate  more  freely, 
and  after  a  time  to  become  sensibly  cooler  than  the  other. 

137.  Application  to  Common  Experience. — We  may 
gather  from  the  foregoing  principles  many  useful  and  im- 
portant  hints  regarding  facts  of  every-day  life.      Thus 
we  learn  why  the  polished  fire-irons,  which  stand  beside  a 
fire,  are  not  inconveniently  heated.     The  heat  which  falls 
upon  them  is  reflected  in  a  great  measure  by  the  polished 
metal.      Should  they  be  allowed  to  become  tarnished  the 
reflection  is  not  so  complete,  and  they  become  heated. 
The  polish,  therefore,  of  fire-irons  is  not  only  ornamental, 
but  contributes  largely  to  comfort  in  handling  them.     It 


124  HEAT. 

is  of  advantage  that  the  interior  of  a  screen  placed  behind 
roasting  meat  be  kept  clean  and  polished,  for  then  it  is  a 
good  reflector,  and  aids  materially  the  cooking  process. 

Certain  parts  of  a  steam  engine  ought  to  be  highly 
polished,  not  so  much  for  appearance'  sake,  but  as  a  most 
effectual  means  of  retaining  the  heat  of  the  steam,  thus 
preventing  loss  by  condensation.  A  stove  ought  to  have 
its  exterior  surface  rough  and  well  blackened,  so  as  to  allow 
radiation  to  take  place  freely.  A  tea-kettle,  on  the  other 
hand,  ought  to  be  well  brightened  up  so  as  to  diminish 
radiation,  and  thus  tend  to  retain  the  heat  of  the  water  as 
long  as  possible.  Should  a  "cosy"  be  used  for  a  tea-pot, 
it  ought  to  be  made  to  fit  loosely,  for  then  the  radiation 
is  much  impeded. 

138.  Absorbing  Power  of  Bodies  —  Reciprocity  of 
Radiation  and  Absorption. — By  the  absorbing  power  of  a, 
body  for  heat  is  meant  that  quality,  in  virtue  of  which  it 
allows  heat  to  pass  into  its  mass.  The  heat  which  falls 
upon  a  body  is  in  part  absorbed  and  in  part  reflected.  All 
the  reflected  portion,  however,  is  not  reflected  regularly, 
that  is,  it  does  not  follow  the  ordinary  law  of  reflection 
(Art.  36);  part  of  it,  as  in  the  case  of  light,  is  irregularly 
reflected,  and  follows  110  particular  law — it  is  called  scat- 
tered or  diffused  heat.  We  may  infer  from  this  that  a 
body  which  is  a  good  reflector  of  heat  is  a  bad  absorber, 
and  vice  versd.  This  has  been  corroborated  by  experi- 
ment. 

Again,  it  has  been  found  that  the  two  qualities  of 
radiation  and  absorption  are  reciprocal,  that  is,  a  body 
wjiich  is  a  good  radiator  of  heat  is  also  a  good  absorber, 
and  one  which  is  a  bad  radiator  is  also  a  bad  absorber. 

To  ascertain  the  relative  absorptive  powers  of  different 
kinds  of  cloth,  Dr.  Franklin  made  the  simple  experiment 
of  putting  a  number  of  pieces  on  snow  as  it  lay  on  the 
ground.  These  were  exposed  for  a  certain  time  to  the 
sun's  rays,  and  the  depths  to  which  they  severally  sank  in 
that  time  were  noted.  He  found  those  pieces  that  were 
dark  in  colour  sank  deepest  in  the  snow,  while  those  that 


REFRACTION    OF    HEAT.  125 

were  light-coloured  sank  least,  from  which  he  inferred  that 
the  former  possessed  the  greatest  power  of  absorption, 
and  the  latter  the  least.  Hence  appears  the  importance 
of  attending  to  the  particular  colour  of  clothing  which 
•should  be  worn  in  the  different  seasons.  Thus,  the  worst 
colour  of  cloth  we  can  wear  in  winter  is  black;  for,  being  a 
powerful  radiator,  it  tends  to  carry  off  the  heat  from  the 
body.  In  summer,  again,  a  light-coloured  dress  is  the 
most  desirable ;  for,  being  a  good  reflector  and  a  bad  ab- 
sorber, it  shields  the  body  from  the  influence  of  the  sun. 

The  discovery  ships  of  Captain  Parry,  it  is  said, 
during  the  severe  winter  which  was  spent  at  Melville 
Island,  were  so  rigidly  frozen  in  as  to  render  it  extremely 
doubtful  whether  the  influence  of  the  summer's  sun 
would  be  sufficient  to  relieve  them.  To  ensure  an  exit, 
the  method  was  adopted  of  strewing  ashes  and  soot  in 
a  line  from  the  ships  to  seaward.  The  consequence  was 
that  these  substances,  by  their  great  absorption  of  the 
sun's  rays,  dissolved  the  subjacent  ice,  thus  forming  a 
passage  for  the  ships  through  the  solid  ice  all  around. 

In  some  of  the  more  mountainous  districts  of  Europe, 
where  the  snow  would  lie  so  long  as  to  retard  cultiva- 
tion, the  peasantry  have  recourse  to  the  plan  of  strewing 
a  quantity  of  earth  upon  the  snow ;  this,  by  its  great 
absorptive  power,  assists  materially  towards  clearing 
the  ground. 

139.  Refraction  of  Heat. — That  heat,  like  light,  can 
be  refracted,  is  plain  from  the  simple  expedient  of  con- 
centrating the  sun's  rays  by  a  burning-glass.  Experiment 
proves  that  a  beam  of  radiant  heat  is  made  up  of  rays 
of  different  degrees  of  refrangibility.  Most  sources  of 
heat  emit  heat  rays,  which  are  partly  luminous  and 
partly  obscure,  and  those  differ  from  each  other  in 
regard  to  their  refractive  capabilities. 

A  bottle  of  water,  acting  like  a  lens,  has  been  known 
to  converge  the  sun's  rays  to  such  an  extent  as  to  cause 
conflagration.  So  also,  it  is  said,  that  in  greenhouses 
drops  of  water  on  the  plants  sometimes  exercise  such 


126  HEAT. 

convergence   on   the  solar  beams,  as  to  burn  tip  the 
leaves. 

140.  Diathermancy.  —  By  this  term  is  meant  the 
power  of  a  body  to  transmit  radiant  heat.  It  bears  the 
same  relation  to  radiant  heat  that  transparency  does  to 
light.  A  body,  however,  which  is  transparent  to  light, 
does  not  necessarily  possess  diathermancy.  Thus  a  sheet 
of  ice,  though  transparent,  does  not  transmit  much  heat. 

The  diathermic  power  varies  much  in  different  bodies. 
The  following  table  exhibits  some  of  the  results  obtained 
by  Melloni,  whose  researches  on  this  subject  have  been 
very  extensive : — 

SOLIDS. 

Name  of  substance.  Transmission.' 

(Thickness  =  roth  of  an  inch).          (Percentage  of  the  total  radiation). 

Rock-salt 92-3 

Fluor-spar 72 

Glass 39 

Felspar 23 

Aluin 9 

Ice G 

LIQUIDS. 

(Thickness  =  '36  in.) 

Bisulphide  of  carbon 03 

Sulphuric  acid 17 

Distilled  water 11 

It  appears  from  this  table  that  rock-salt  has  a  high 
diathermic  power,  about  2i  times  that  of  glass,  10  times 
that  of  alum,  and  15  times  that  of  ice.  Melloni  has 
found  that  the  power  of  transmission  varies  in  different 
bodies  with  the  source  of  heat — rock-salt,  however,  form- 
ing an  exception. 

The  two  substances,  rock-salt  and  alum,  are  used  to 
separate  the  light  and  heat  which  radiate  from  the  same 
source.  The  former,  when  covered  with  lampblack, 
transmits  the  heat  freely,  but  arrests  the  light;  whilst 
the  latter  arrests  the  heat  and  transmits  the  light. 

Aqueous  vapour,  though  diathermic  for  heat  from 
luminous  rays,  is  not  so  for  heat  from  obscure  rays. 


DIATHERMANCY.  127 

Tyndall  has  proved  this  by  a  series  of  careful  experi- 
ments. He  remarks  in  regard  to  it,  "No  doubt  can 
exist  of  the  extraordinary  opacity  of  this  substance  to  the 
rays  of  obscure  heat;  particularly  such  rays  as  are 
emitted  by  the  earth  after  being  warmed  by  the  sun. 
Aqueous  vapour  is  a  blanket  more  necessary  to  the  veget- 
able life  of  England  than  clothing  is  to  man.  Remove  for 
a  single  summer  night  the  aqueous  vapour  from  the  air 
which  overspreads  this  country,  and  you  will  assuredly 
destroy  every  plant  capable  of  being  destroyed  by  a  freez- 
ing temperature.  The  warmth  of  our  fields  and  gardens 
would  pour  itself  unrequited  into  space,  and  the  sun  would 
rise  upon  an  island  held  fast  in  the  iron  grip  of  frost."* 
He  has  also  shown  that  air,  more  or  less  charged  with 
aqueous  vapour,  may  exercise  from  30  to  70  times  the 
absorptive  effect  of  dry  air.  Hence  appears  the  cause  of 
the  extreme  cold  met  with  in  the  upper  regions  of  the 
atmosphere,  where  the  quantity  of  aqueous  vapour  is  much 
reduced. 

It  is  worthy  of  note  that  glass  is  capable  of  trans- 
mitting luminous  heat,  but  greatly  retards  the  passage  of 
obscure  heat.  As  the  sun's  radiation  consists  in  a  large 
measure  of  luminous  heat-rays,  we  can  understand  why  the 
panes  of  glass  in  a  window  are  not  much  heated  even  by 
brilliant  sunshine.  By  their  contact  with  different  ob- 
jects, however,  they  are  changed  into  obscure  rays,  and 
as  such  cannot  re-traverse  the  glass.  Hence  the  reason 
why  a  room  exposed  to  a  summer's  sun  gets  so  heated — 
the  glass,  though  allowing  the  sun's  heat  to  pass  in,  serves 
as  a  barrier  to  its  getting  out.  Hence  also  the  high  tem- 
perature of  green-houses  and  photographic  apartments 
after  strong  sunshine. 

The  effect  of  a  glass  screen  placed  in  front  of  a  fire  is 
well  known.  The  calorific  rays  being  in  a  large  measure 
intercepted,  the  screen  becomes  warm,  but  radiates  its  heat 
in  all  directions,  and  thus  the  heat  of  the  fire  is  miti- 
gated, though  at  the  same  time  we  have  its  pleasant  light. 
*  Tyndall  on  Heat  as  a  Mode  of  Motion,  p.  372. 


128  HEAT. 


QUESTIONS. 

1.  What  is  meant  by  (1)  the  linear,  and.  (2)  the  cubical  co-effi- 
cient of  expansion  ?    Is  there  any  relation  between  them  ?  if  so, 
state  what  it  is. 

2.  Convert  -15°C.  into  the  Fahrenheit  scale;  and  12° R.  into 
the  centigrade.  'An*.  (1)  5°,  (2)  15°. 

3.  At  what  temperature  is  the  density  of  water  a  maximum  ? 
Water  expands  in  freezing :  is  this  property  peculiar  to  water  ? 

4.  Explain  the  process  by  which  a  lake  is  frozen  over. 

5.  Explain  the  trade-winds. 

6.  Define  "specific  heat."     Describe  some  method  of  deter- 
mining the  specific  heat  of  a  body. 

7.  A  pound  of  mercury  at  102°  is  immerseE  in  a  pound  of 
water  at  40° ;  how  much  will  the  temperature  of  the  water  be 
raised,  assuming  the  specific  heat  of  mercury  to  be  '03  ? 

Am.  2°. 

8.  What  is  meant  by  "  latent  heat  ?"   What  is  the  latent  heat 
of  water  ?     Explain  clearly  what  the  number  implies. 

9.  How  many  pounds  of  ice  at  0°C.  can  be  melted  by  5  pounds 
of  steam  at  100° (J.  ?  Am.  40. 

10.  If  1  pound  of  steam  at  100°  C.  be  mixed  with  49  pounds  of 
water  at  15°C.,  how  much  will  the  temperature  of  the  water  be 
raised?  Ans.  12£°. 

11.  Give  Prevost's  theory  of  exchanges. 

12.  Describe  some  experiment  for  freezing  water  by  evapora- 
tion. 

13.  Distinguish  between  the  convection  and  conduction  of  heat. 

1 4.  Give  the  theory  of  combustion  of  a  gas  flame ;  and  explain 
the  action  of  a  Bunsen  lamp. 

15.  The  rays  of  the  sun  in  passing  through  a  window  do  not 
sensibly  heat  the  panes  of  glass;  but  a  glass  screen  placed  in 
front  of  a  fire  becomes  warm.     How  do  you  account  for  these 
effects? 


SELECTION  OF  QUESTIONS 

PROPOSED   AT   THE 

EXAMINATIONS  OF  THE  GOVERNMENT  DEPARTMENT 

OF  SCIENCE  AND  ART,  FROM  1867  TO  1872, 

WITH  THEIR  SOLUTIONS. 


ACOUSTICS. 

1.  What  do  you  understand  by  a  wave,  of  sound  ? 

By  a  wave  of  sound  is  meant  an  undulation,  or  wave-like  mo- 
tion, communicated  to  the  particles  of  air  in  consequence  of  the 
vibration  of  the  sounding  body.  It  consists  of  two  parts,  one 
in  which  the  air  is  condensed,  called  a  condensation,  and  the 
other  in  which  the  air  is  rarefied,  called  a  rarefaction. 

Whilst  the  undulation  or  wave  is  transmitted  through  the  air, 
the  aerial  particles  themselves  have  but  a  very  small  motion  to 
and  fro,  in  the  direction  in  which  the  sound  is  propagated.  Such 
oscillatory  movements  are  necessarily  attended  by  condensations 
and  rarefactions. 

2.  Describe  the  manner  in  which  sound  is  propagated  through 
air,  water,  or  wood. 

When  a  body  in  air  emits  sound,  it  moulds  the  surrounding 
air  into  undulations  or  waves.  These  waves  consist  of  alternate 
condensations  and  rarefactions  of  the  air  caused  by  the  vibration 
of  the  sounding  body,  and  it  is  in  consequence  of  such  waves 
entering  our  ears  that  we  derive  the  sensation  of  sound. 

A  similar  effect  is  believed  to  take  place  in  water  or  wood. 
The  sound  is  propagated  through  either  substance  in  the  form  of 
waves,  in  which  the  molecules  have  a  limited  motion  to  and  fro. 

3.  The  velocity  of  sound  in  water  is  much  greater  than  its  velocity 
in  air.      Why  is  this  the  case  ? 

The  velocity  of  sound  in  any  medium  depends  upon  the  elasticity 
and  density  of  the  medium,  or,  rather,  upon  the  relation  which 
the  former  bears  to  the  latter.  Now,  in  the  case  of  water,  this 
relation  is  higher  than  in  air,  and  hence  the  velocity  of  sound 
is  greater. 

SE  j 


130  QUESTIONS. 

4.  You  fire  a  shot  before  a  cliff,  and  hear  the  echo  five  seconds 
afterwards,  what  is  the  cliff's  distance  from  the  centre  of  explosion  ? 

Sound  travels  at  the  rate  of  1125  feet  per  second  (temperature 
~62°F.).  In  five  seconds  it  will  therefore  travel  over  1125x5, 
or  5625  feet,  that  is,  in  this  time  the  sound  of  the  explosion  in 
going  to,  and  returning  from,  the  cliff,  will  travel  over  this  space  ; 
hence  the  distance  of  the  cliff  =  «Mi  =  2812^  feet— Answer. 

5.  How  do  you  suppose  the  human  voice  to  be  produced  ?     What 
occurs  in  the  case  of  your  voice  when  you  sing  high  notes  and  low 
notes  ? 

The  trachea,  or  wind-pipe,  tapers  towards  the  top,  leaving  a 
narrow  slit-like  opening  between  the  membranes,  termed  the 
glottis.  The  air  passing  from  the  lungs  with  sufficient  force,  in 
escaping  through  the  glottis  throws  the  membranes  into  vibration, 
and  thus  it  is  that  voice  is  produced. 

Notes,  or  sounds  of  different  pitch,  are  produced  by  the 
muscles,  or  vocal  chords,  as  they  are  called,  acting  upon  the  mem- 
branes enclosing  the  glottis,  either  in  the  way  of  tightening  or 
relaxing  them,  and  this  is  effected  by  the  simple  act  of  volition 
on  our  part. 

6.  Air  and  hydrogen  gas  are  urged  in  succession   through  the 
same  organ-pipe.     Describe  the  effects  and  explain  them. 

Air,  when  urged  through  an  organ-pipe,  gives  a  note  of  a 
certain  pitch.  When  hydrogen  gas  is  urged  through  the  pipe 
with  the  same  force  it  produces  a  note  of  a  higher  pitch.  This 
results  from  the  velocity  of  sound  being  greater  in  hydrogen  than 
in  air,  and  hence  the  number  of  vibrations  per  second  executed 
in  the  former  case  is  greater  than  in  the  latter. 

7.  How  are  musical  sounds  produced  ?   On  what  do  the  pitch  and 
the  intensity  of  a  musical  sound  depend  ? 

A  musical  sound  is  produced  by  periodic  impulses  imparted  to 
the  air  by  the  sounding  body,  that  is,  by  impulses  which  succeed 
each  other  after  perfectly  equal  intervals  of  time. 

Pitch  depends  entirely  upon  the  number  of  vibrations  executed 
per  second. 

Intensity,  again,  depends  upon  the  amplitude  of  the  vibrations, 
or  the  amount  of  disturbance  given  to  the  air-particles  in  conse- 
quence of  these  vibrations. 

8.  What  are  the  changes  of  temperature  which  occur  in  a  wave  of 
sound  ? 

A  wave  of  sound  consists  of  two  parts,  in  one  of  which  the  air 
is  condensed,  and  in  the  other  rarefied.  Now,  when  air  is  con- 
densed heat  is  evolved,  and  when  rarefied  cold  is  produced.  In 
the  condensed  portion  of  the  wave,  therefore,  the  air  is  above, 
and  in  the  rarefied  portion  below,  its  average  temperature.  These 


QUESTIONS.  131 

changes  of  temperature,  however,  though  augmenting  the  velocity 
of  sound,  do  not  affect  the  general  temperature  of  the  air 
through  which  the  sound  passes. 

9.  State  the  likeness  that  exists  between  sound  and  light  as  regards 
reflection  and  refraction. 

(1)  Reflection, — Sound  and  light  obey  the  same  law,  viz.,  the 
angle  of  reflection  is  equal  to  the  angle  of  incidence.     Their 
similarity  in  this  respect  is  proved  in  several  ways.     Thus,  in 
an  elliptical  whispering  gallery,  whilst  the  exhibitor  places  him- 
self in  one  focus,  the  observer,  by  going  to  the  other,  can  hear 
the  slightest  whisper.     So  also  if  two  large  elliptical  metallic 
reflectors  be  so  placed  as  to  have  their  foci  in  the  same  position  as 
they  would  be  were  the  ellipse  (or  rather  ellipsoidal  shell)  com- 
plete, a  lamp  set  in  one  focus  would  have  its  light  concentrated  in 
the  other,  and  an  image  of  the  lamp  would  be  formed  there. 

Or,  again,  by  taking  a  concave  spherical  reflector,  and  placing 
a  watch  immediately  in  front,  its  ticking  may  be  heard  distinctly 
by  a  person  adjusting  his  ear  at  the  focus  some  distance  off.  A 
lamp,  in  like  manner,  placed  in  the  same  position,  will  have  an 
image  of  itself  formed  at  precisely  the  same  point  as  that  at 
which  the  ticking  of  the  watch  was  heard. 

(2)  Refraction. — Sound  and  light  can  also  be  refracted  or  bent 
out  of  their  original  course.     A  common  method  of  refracting 
light  is  to  use  a  glass  lens.     In  the  case  of  sound,  it  can  be 
refracted  by  using  a  thin  india-rubber  balloon  filled  with  carbonic 
acid  gas.      A  watch  placed  at  one  side  of  it  can  be  distinctly 
heard  at  the  other,  near  the  point  where  the  sound-waves  are 
converged. 

10.  Wherein  does  the  transmission  of  sound  through  a  smooth 
tube  differ  from  its  transmission  through  the  open  air  ? 

The  sound  waves  which  proceed  from  a  sonorous  body  gradu- 
ally enlarge  as  they  recede  from  it,  in  open  air.  When  they  are 
transmitted  through  a  smooth  tube,  they  are  prevented  from 
thus  enlarging,  and,  in  addition,  are  reflected  from  side  to  side 
of  the  tube  till  they  eventually  emerge  at  the  end.  In  conse- 
quence of  this,  the  slightest  whisper  can  be  heard  through  a  long 
tube. 

11.  What  is  the  influence  of  heat  and  cold  upon  the  velocity  of 
sound  in  air  ? 

If  the  density  of  the  air  be  diminished,  the  velocity  of  sound 
is  increased,  and  if  the  density  be  increased,  the  velocity  is 
diminished  (the  elasticity  remaining  the  same).  Now  the  eifect 
of  heat  is  to  diminish  the  density  of  the  air,  and  of  cold  to 
increase  it.  Hence  heat  increases  the  velocity  of  sound,  and  cold 
diminishes  it. 


132  QUESTIONS. 


LIGHT. 

1.  A  straight  stick  placed  obliquely  in  the  water  appears  bent  at 
the  surface  of  the  water ,  a  ray  of  light  entering  the  water  obUqudy 
is  also  bent  at  the  surface;  are  the  stick  and  the  beam  bent  in  the 
same  manner  or  not  ? 

No.  The  stick  is  bent  upwards,  or  from  the  perpendicular, 
whilst  a  ray  of  light,  entering  the  water  obliquely,  is  bent  toward* 
the  perpendicular ;  because  in  the  latter  case  the  ray  passes  from 
a  rare  medium  into  a  denser. 

2.  Describe  an  experiment  to  prove  that  out  of  a  mixture  of  light 
of  various  colours  you  can  produce  colourless  or  white  light. 

Take  a  circular  disc  of  cardboard  and  divide  it  into  sectors, 
having  the  same  proportion  as  the  spaces  which  the  different 
colours  of  the  solar  spectrum  occupy.  Then  colour  these  sectors 
with  the  different  hues  successively,  viz.,  red,  orange,  yellow, 
green,  blue,  indigo,  and  violet. 

If  now  the  disc  be  attached  to  a  revolving  apparatus,  and 
whirled  rapidly  round,  the  colours  will  be  blended  together,  and 
will  produce  a  white  appearance.  The  experiment  is  founded  on 
the  principle  of  the  "persistence  of  impressions  on  the  retina." 

3.  State  what  you  know  regarding  the  form  and  use  of  spectacles. 

(1)  Form. — Spectacle  glasses  are  either  converging  or  diverging 
lenses.     Of  each  class  there  are  three  kinds,  which  have  names 
assigned  them  from  the  nature  of  their  bounding  surfaces.     A 
double  convex  lens  is  a  type  of  the  converging  class,  and  a  double 
concave  lens  of  the  diverging  class. 

(2)  Use. — In  order  to  have  distinct  vision,  the  image  of  an 
object  must  be  thrown  upon  the  retina.     The  object  of  spectacles 
is  to  enable  the  eye  to  accomplish  this.     In  far-sighted  persons, 
the  eye  has  too  little  convergent  power,  and  cannot  concentrate 
the  rays  of  light  upon  the  retina.      On  the  other  hand,  in  short- 
sighted persons,  the  eye  has  too  much  convergent  power,  and 
brings  the  rays  to  a  focus  too  soon,  or  in  front  of  the  retina.    The 
remedy  in  the  former  case  is  to  use  a  converging  glass,  and  in 
the  latter  a  diverging  glass,  of  sufficient  *  brength  to  enable  the 
eye  to  concentrate  the  rays  exactly  upon  the  retina. 

4.  State  what  you  know  regarding  the  production  of  the  colours 
of  flowers.      Why,  for  example,  is  a  rose  red  and  grass  green  ? 

The  colour  of  an  object  depends  upon  the  treatment  to  which 
the  rays  of  light  falling  upon  it  are  subjected.  Sun-light  is  not 
homogeneous,  but  is  composed  of  seven  distinct  kinds  of  light. 
Colour  is  owing  to  certain  of  these  constituents  being  absorbed 
or  quenched  by  the  object,  the  remaining  ones  being  reflected  and 
giving  to  the  object  the  colour  which  it  appears  to  possess. 


QUESTIONS.  133 

Thus,  &  rose  is  red  because  all  the  constituents  of  white  light, 
except  the  red  (which  is  reflected),  are  absorbed ;  so  also  the 
grass  is  green,  because  the  green  colour  is  reflected  by  the  grass, 
the  other  constituents  being  absorbed. 

5.  A  cloud  is  composed  of  transparent  water-particles;  but,  if 
transparent,  why  are  clouds  able  to  Intercept  so  much  of  the  sun's 
liyht  ? 

The  water-particles,  though  transparent,  are  not  perfectly  so  ; 
part  of  the  light  falling  upon  them  is  absorbed,  but  the  greater 
part  is  broken  up  and  scattered  in  all  directions  by  multiplied 
reflections.  There  is  consequently  a  loss  of  light,  and  this  loss 
will  be  greater  the  denser  the  cloud. 

It  is  for  the  same  reason  that  a  mass  of  pounded  glass  becomes 
practically  opaque  when  in  sufficient  thickness. 

6.  /  wish  you  to  compare  the  light  of  a  candle  Jlame  with  that  of 
a  gas  Jlame  of  the  same  size.     How  would  you  determine  and  ex- 
2)ress,  numerically,  the  relative  intensities  of  the  two  ligJits  ? 

The  relative  intensities  of  two  different  sources  of  light  may 
be  determined  by  what  is  called  ' '  the  shadow  test. "  The  method 
is  this :  In  a  darkened  room  place  the  two  lights  in  front  of  a 
screen,  and  between  them  and  the  screen  place  a  rod  or  stick ; 
now  adjust  the  lights  at  such  distances  as  that  the  shadow  of 
the  stick  may  appear  equally  illuminated  when  viewed  from  the 
other  side  of  the  screen.  Then  measure  these  distances.  Suppose 
they  are  for  the  candle  and  gas  flame  5  feet  and  8  feet  respectively. 
Now,  as  the  intensities  are  directly  proportional  to  the  squares  of 
the  distances,  we  have 

Intensity  of  candle  :  intensity  of  gas  :  :  25  :  64 ; 

in  other  words,  the  gas  would   have  nearly  2?-  times  the  il- 
luminating effect  of  the  candle, 

7.  A  large  concave  mirror  is  placed  before  you.     You  see  your 
image  first  inverted  in  the  air;  you  change  your  distance  from  the 
mirror,  and  find  that  in  a  certain  position  your  image  vanishes; 
again  you  change  your  position,  and  find  your  image  erect.      Under 
what  circumstances  are  these  effects  observed?    State  whether  the 
images  observed  are  of  greater  or  less  size  than  yourself,  and  give 
the  reason  of  the  increase  or  diminution. 

When  the  image  of  the  object  is  seen  inverted  in  the  air,  the 
object  itself  is  beyond  the  centre  of  curvature  of  the  mirror.  The 
image  (real)  in  this  case  is  formed  between  the  principal  focus  ami 
the  centre  of  curvature,  and  is  smaller  than  the  object,  because  its 
distance  from  the  centre  of  curvature  is  less  than  the  distance 
of  the  object  from  the  same  point. 

When  the  image  vanishes,  the  object  coincides  with  the  centre 
of  curvature,  for  in  that  position  the  rays  from  the  object  are 


134  QUESTIONS. 

reflected  directly  back,  and  the  place  of  the  object  is  the  focus 
of  the  image. 

Lastly,  when  the  image  (now  virtual)  is  seen  erect,  the  object 
is  placed  between  the  principal  focus  and  the  mirror.  This 
image  is  larger  than  the  object,  because  its  distance  from  the 
centre  of  curvature  is  greater  than  the  distance  of  the  object. 

8.  Describe  the  circumstances  under  which  total  reflection  takes 
place.     Supposing  your  eyes  were  placed  under   the  water  of  a 
lake,  what  appearance  do  you  suppose  a  man  standing  on  the  brink 
of  the  lake  ivould  present  to  you  ? 

When  a  ray  of  light  passes  from  a  dense  medium  into  a  rarer, 
it  is  refracted  from  the  perpendicular. 

If  the  angle  of  incidence  be  gradually  increased,  it  will  at 
last  attain  such  a  magnitude  as  that  the  emergent  ray  becomes 
nearly  parallel  to  the  surface  of  the  water.  This  angle  is  called 
the  limiting  or  critical  angle  of  refraction.  For  water  and  air 
this  angle  is  48^°.  If,  therefore,  the  incident  ray  make  a  greater 
angle  than  this,  it  will  not  emerge  from  the  water,  but  will  be 
reflected  at  the  surface,  following  the  ordinary  law  of  reflection. 

As  a  ray  of  light  passing  from  air  into  water  is  refracted 
towards  the  perpendicular,  an  eye  receiving  that  ray  will  take  it 
as  coming  along  the  line  of  prolongation  of  the  refracted  ray; 
hence,  on  the  supposition  stated,  the  man,  as  well  as  the  brink 
of  the  lake,  will  appear  lifted  up. 

9.  What  is  meant  by  the  scattering  of  light,  and  what  by  its  regular 
reflection? 

The  scattering  of  light  means  the  irregular  reflection  of  light 
from  the  surfaces  of  bodies,  in  consequence  of  which  we  sec  them 
or  become  aware  of  their  existence. 

By  the  regular  reflection  of  light  is  meant  such  reflection  as 
we  have  from  mirrors  or  polished  reflectors ;  and,  where  the  law 
holds  good,  that  the  angle  of  reflection  is  equal  to  the  angle  of 
incidence. 

If  a  mirror  reflected  all  the  light  which  fell  upon  it  regularly, 
the  mirror  itself  would  be  invisible ;  it  is  in  consequence  of  the 
scattering  of  some  of  the  light  that  we  are  enabled  to  see  it. 

10.  I  fill  two  cups  of  the  same  deptli  with  two  different  liquids, 
and  notice  two  things:  firstly,   both  cups  appear  shallower  than 
when  they  are  empty;  and,  secondly,  one  of  them  appears  shallower 
than  the  other.     Explain  the  observation. 

The  rays  from  the  bottom  of  each  cup,  in  emerging  from  the 
liquid,  are  refracted  from  the  perpendicular,  or  towards  the 
surface  of  the  liquid.  These  rays  therefore  enter  the  eye  as  if 
they  came  along  the  prolongations  of  the  lines  in  which  they  are 
refracted.  The  eye  receives  these  rays  as  if  they  came  from 
points  above  the  bottom  of  each  cup;  hence  each  bottom  appears 


QUESTIONS.  135 

raised;  in  other  words,  both  cups  appear  shallower  than  they 
really  are. 

That  cup  appears  shallower  which  contains  the  denser  liquid, 
because  the  rays  are  subjected  to  a  greater  amount  of  refraction. 

11.  Describe,  clearly  an  experiment  by  which  white  light  can  be 
resolved  into  the  differently  coloured  lights  which  compose  the  white. 
Describe  also  an  experiment  by  which  the  colours  can  be  recom- 
pounded. 

A  beam  of  sun-light  is  admitted  through  an  aperture  made  in 
the  shutter  of  a  darkened  room;  a  prism  is  interposed  in  its 
course,  and  a  screen  is  placed  at  some  distance  from  it.  An 
elongated  image  of  the  sun  is  found  depicted  on  the  screen,  and 
coloured  after  the  following  manner  (commencing  with  the  lowest 
colour) :  red,  orange,  yellow,  green,  blue,  indigo,  and  violet. 
The  image  thus  formed  is  called  the  solar  spectrum. 

For  the  answer  to  the  remaining  part,  see  Question  2. 

12.  State  the  likeness  that  exists  betiveen  light  and  radiant  heat  as 
regards  reflection,  refraction,  and  transmission. 

(1)  Reflection. — Both  obey  the  same  law,  viz.,  that  the  angle 
of  reflection  is  equal  to  the  angle  of  incidence.      This  is  well 
proved  by  placing  two  concave  spherical  reflectors  directly  oppo- 
site each  other,  and  placing  a  lamp  or  red-hot  iron  ball  in  the 
principal  focus  of  one  of  the  reflectors.      It  is  found  that  the 
light  or  heat  is  concentrated  in  the  principal  focus  of  the  other 
reflector,  owing  to  the  reflection  from  the  two  mirrors. 

(2)  Refraction. — A  convex  lens  of  glass  is  a  common  means  of 
refracting  light,  so  as  to  converge  it  to  a  focus.     Radiant  heat 
may  also  be  concentrated  by  a  lens  of  this  kind,  but  better  still 
by  a  lens  made  of  rock-salt. 

(3)  Transmission. — Light  is  transmitted  through   a  plate  of 
glass,  so  also  is  heat,  but  not  with  such  readiness  as  through  a 
plate  of  rock-salt.     This  latter  substance,  whilst  it  offers  resist- 
ance to  the  transmission  of  light,  gives  a  ready  passage  to  heat. 

13.  Light  issues  from  a  luminous  globe  twelve  inches  in  diameter, 
and  falls  upon  a  second  opaque  globe  six  inches  in  diameter,  show 
by  a  diagram  the  kind  of  shadow  cast  by  the  latter. 

By  examining  carefully  the  diagram  in  Art.  30,  the  student 
will  have  no  difficulty  in  constructing  the  diagram  for  this  ques- 
tion. 

N.B. — There  are  both  the  umbra  and  the  penumbra  formed. 

14.  Looking  through  a  red  glass  at  the  white  body  of  the  sun  you 
see  it  red,  in  what  way  does  the  red  glass  act  upon  the  light  so  as  to 
produce  this  impression  ? 

The  sun's  light  in  traversing  the  glass  is  decomposed,  all  the 
constituents  being  quenched,  except  the  red  light ;  hence  the  red 
appearance  given  to  the  sun. 


136  QUESTIONS. 


HEAT. 

1.  What  do  you  understand  by  radiant  heat  ? 

Radiant  heat  is  the  heat  emitted  by  a  body  through  intervening 
space.  The  heat  of  the  sun,  the  heat  of  a  fire,  the  heat  of  a  stove, 
etc.,  are  examples. 

The  heat  of  a  body  is  believed  to  be  owing  to  a  state  of  vibra- 
tion among  its  particles.  This  vibratory  motion  a  heated  body 
can  communicate  to  the  surrounding  ether,  which  in  turn  affects 
other  bodies,  and  thus  heat  is  said  to  be  capable  of  radiating  from 
one  body  to  another. 

2.  How  is  the  bulk  of  a  body  usually  affected  by  heat?     Are 
there  any  exceptions  to  the  general  rule  ?    If  so,  state  such  excep- 
tions, and  describe  the  circumstances  under  which  the  exception 
appears. 

A  body  is  enlarged  in  bulk  by  the  addition  of  heat,  and 
diminished  by  the  abstraction  of  heat.  The  general  rule  may  be 
shortly  stated  thus  :  "Heat  expands,  and  cold  contracts." 

There  are  some  exceptions  to  this  principle.  Water  when 
cooled  down  to  about  40°  F.  contracts,  so  far  obeying  the 
rule ;  at  this  point,  however,  all  contraction  ceases.  When  cooled 
down  below  this  temperature  it  expands,  and  it  does  so  at  an 
increasing  rate  as  the  freezing-point  is  approached. 

Certain  metals,  when  melted,  undergo  expansion  on  solidifica- 
tion— bismuth  and  cast-iron  are  examples;  hence  the  precision 
with  which  cast-iron  takes  the  impression  of  a  mould. 

Another  exception  is  found  in  stretched  india-rubber.  Thus, 
if  an  india-rubber  band  support  a  weight,  and  the  position  of  tlio 
weight  be  observed,  when  the  band  is  heated  the  weight  is  raised, 
owing  to  contraction  on  the  part  of  the  rubber. 

3.  If  a  liquid  be  heated  at  the  bottom,  how  is  the  heat  distributed 
through  the  liquid  ?   If  heated  at  tJie  top,  how  is  the  heat  propagated  ? 

When  a  liquid  is  heated  at  the  bottom,  the  heat  is  distributed 
through  the  liquid  by  convection.  The  particles  of  the  liquid 
next  the  heating  source  becoming  warm,  expand  and  rise  to  the 
surface.  Other  particles  take  their  place,  which  in  turn  also  ex- 
pand and  rise.  There  is  thus  a  circulation  maintained  in  the 
liquid,  in  virtue  of  which  the  warm  particles  just  escaped  from 
the  bottom  are  constantly  ascending,  whilst  the  colder  particles 
are  as  constantly  descending  to  supply  their  place. 

If  the  liquid  be  heated  at  the  top  the  heat  is  found  to  make  its 
way  very  slowly  downwards,  and  this  it  can  only  do  by  the  heat 
being  propagated  from  particle  to  particle,  or  by  the  process  of 
conduction. 


QUESTIONS.  137 

4.  What  is  meant  by  the  boiling  point  of  a  liquid?     What  is  the 
boiling  point  of  water,  and  how  could  water  be  heated  above  its 
ordinary  boiling  point  ?    How  is  the  boiling  point  ajfected  when  we 
ascend  a  mountain? 

The  boiling  point  of  a  liquid  may  be  denned  as  "that  point  at 
which  the  tension  or  elastic  force  of  its  vapour  is  equal  to  the  pres- 
sure which  it  supports. " 

The  boiling  point  of  water  (when  the  barometer  is  30  inches)  is 
212°F.  At  this  temperature,  according  to  the  above  definition, 
the  elastic  force  of  the  vapour,  or  steam,  which  escapes  from  the 
water,  is  equal  to  the  ordinary  pressure  of  the  atmosphere.  By 
subjecting  the  water  to  a  greater  pressure  than  the  ordinary  pres- 
sure of  the  atmosphere,  the  boiling  point  of  water  could  be  raised ; 
in  other  words,  the  water  could  be  heated  above  its  ordinary 
boiling  point.  This  actually  takes  place  in  a  closed  vessel,  such 
as  in  the  boiler  of  a  steam  engine.  The  steam  accumulates  on 
the  surface  of  the  water,  and  exerts  a  greater  pressure  than  that 
of  the  atmosphere ;  the  consequence  is  that  the  water  is  heated 
above  212°F. 

The  boiling  point  of  a  liquid  is  lowered  as  we  ascend  a  mountain, 
because  of  the  diminishing  pressure  of  the  atmosphere.  At  the 
top  of  a  high  mountain,  therefore,  it  may  be  lowered  many 
degrees.  At  the  top  of  Mont  Blanc,  for  example,  water  is  found 
to  boil  at  1SO°F. 

5.  Give  a  clear  statement  of  what  you  understand  by  the  radiation, 
reflection,  and  absorption  of  heat. 

Radiation  is  the  passage  of  heat  from  one  body  to  another 
through  intervening  space,  or  it  may  be  stated  to  be  "the  com- 
munication of  motion  from  the  particles  of  a  heated  body,  to  the 
ether  in  which  these  particles  are  immersed,  and  through  which 
the  motion  is  propagated." 

Reflection  is  the  bending  back  of  radiant  heat  into  the  medium 
through  which  it  came  to  meet  the  reflector.  Radiant  heat  can 
be  reflected  from  bright  metallic  reflectors,  whether  plane  or 
curved,  and  follows  the  ordinary  law  of  the  reflection  of  light. 

Absorption  is  the  receiving  or  taking  in  of  heat  by  a  body  from 
a,  warmer  one.  The  two  qualities  of  radiation  and  absorption  are 
reciprocal ;  in  other  words,  the  radiating  power  of  a  body  is  just  in 
proportion  to  its  absorbing  power. 

6.  I  place  water,  alcohol,  and  ether,  all  of  the  same  temperature, 
on  my  hand  in  succession.     I  experience  a  certain  cold  from  the 
water,  a  greater  cold  from  the  alcohol,  and  a  still  greater  cold  from 
the  ether.     State  the  cause  of  these  differences. 

It  is  the  rate  of  evaporation.  When  a  liquid  is  being  evapor- 
ated heat  is  abstracted,  which  becomes  latent  in  the  vapour,  and 
the  amount  of  that  heat  varies  with  the  rate  of  evaporation  of 


138  QUESTIONS. 

the  liquid.  In  the  question,  the  evaporation  being  aided  by  the 
heat  of  the  hand,  there  is  an  abstraction  of  heat  from  the  hand, 
producing  thereby  a  cold  sensation  in  each  case.  But  the  water 
evaporates  slowly,  the  alcohol  more  rapidly,  and  the  ether  more 
rapidly  still ;  hence  the  difference  in  the  sensations. 

7.  A  pound  of  iron  at  a  temperature  of  100°  is  immersed  in  a 
pound  of  ivater  at  a  temperature  of  50° ;  how  many  degrees  will  the 
temperature  of  the  water  be  exalted?    (Note, — Specific  heat  of 

.  iron  —  *!)• 

There  is  here  a  difference  of  temperature  between  the  iron  and 
water  of  50°.  But  the  specific  heat  of  water  is  10  times  that  of 
ron ;  hence  we  have  to  divide  50°  in  the  proportion  of  10  to  1. 

.'.  11  :  1  :  :  50  =  4&,  that  is,  the  water  is  raised  4/j0- 

8.  A  plate  of  rock-salt  if  placed  in  front  of  a  fire  will  not  be 
heated,  while  a  plate,  of  glass  will  be  heated.     A  hot  plate  of  rock- 
salt  held  at  a  short  distance  from  the  face  hardly  warms  the  face, 
tuhile  a  hot  plate  of  glass  does  warm  it.     Explain  these  effects. 

Some  bodies  are  diathermic,  that  is,  allow  heat  to  pass  through 
them  freely;  others  offer  considerable  resistance.  Rock-salt  is 
an  instance  of  the  former  class,  and  glass  of  the  latter.  The  heat 
of  the  fire  therefore  is  transmitted  readily  through  the  plate  of 
rock-salt,  whilst  it  is  largely  arrested  by  the  plate  of  glass ;  hence 
the  difference  of  effect. 

Again,  rock-salt  is  a  bad  radiator  of  heat,  and  glass  is  a  good 
radiator.  The  rock-salt  plate  therefore  radiates  little  heat  towards 
the  face,  whilst  the  glass  plate  radiates  pretty  freely. 

9.  How  is  the  heat  of  a  fire  produced?    How  is  the  heat  of  your 
own  body  produced  ? 

The  heat  of  a  fire  is  produced  by  combustion,  that  is,  by  the 
chemical  combination  of  the  oxygen  of  the  air  with  the  carbon  of 
the  fuel.  Ordinary  coal  consists  mainly  of  carbon  and  hydro- 
gen ;  when  it  is  lighted  the  oxygen  of  the  air  unites  with  the 
carbon  and  hydrogen,  forming  carbonic-oxide,  carbonic  acid,  and 
water  vapour,  at  the  same  time  evolving  heat. 

The  heat  of  the  body  is  also  due  to  combustion;  the  oxygen 
of  the  air  unites  with  the  carbon  elements  of  the  blood  and 
animal  tissue,  evolving  heat,  and  forms  carbonic  acid,  which  is 
being  constantly  exhaled. 

10.  Are  clothes  really  warm  ?    If  not,  why  are  they  sometimes 
called  warm  ?     What  is  the  real  meaning  and  action  of  cool  dresses 
and  warm  dresses  ? 

No.  They  are  popularly  called  warm,  because  the  heat  of  the 
body  is  maintained,  or  prevented  from  being  dissipated,  by  the 
non-conducting  quality  of  the  materials  used  for  clothing. 


QUESTIONS.  139 

Cool  dresses  imply  that  the  textures  used  are  good  conductors 
of  heat,  and  therefore  tend  to  lead  away  the  heat  from  the  body. 
Warm  dresses,  again,  imply  that  the  textures  are  bad  conductors, 
and  therefore  tend  to  preserve  the  heat  of  the  body. 

11.  Explain  tlie  formation  of  dew  and  hoar-frost. 

Dciv. — After  sunset,  the  earth  radiates  the  heat  she  has  received 
during  the  day,  and  as  the  night  advances,  the  cooling  down 
becomes  such  as  to  affect  the  superincumbent  air.  _  That  air 
becomes  also  chilled,  and  is  no  longer  able  to  hold  its  aqueous 
vapour  in  suspension ;  condensation  ensues,  and  the  watery  par- 
ticles are  deposited  on  the  ground.  The  deposition  is  greatest  on 
§rass  and  foliage,  because  of  their  high  radiating  powers.  A 
v^otidy  night  or  a  windy  night  is  unfavourable  to  its  production. 

Hoar-frost. — If  it  so  happen  that,  after  dew  is  deposited,  the 
temperature  of  the  air  sinks  below  the  freezing-point,  then  the 
watery  particles  are  frozen,  and  appear  as  hoar-frost. 

12.  Describe  liow  the  common  mercurial  tJiermometer  is  made  and 
graduated. 

Construction. — A  glass  tube  of  small  and  uniform  bore,  with  a 
bulb  at  the  end,  is  taken,  the  other  end  being  opened  out  into  a 
cup-like  shape.  The  bulb  is  then  held  over  a  flame,  and  when 
the  air  is  sufficiently  expelled,  pure  mercury  is  poured  in.  The 
bulb  is  again  heated  so  as  to  expel  the  air,  and  another  quantity 
of  mercury  is  poured  in,  and  so  on  until  a  sufficient  quantity  is 
introduced.  When  this  is  done,  the  bulb  is  once  more  heated 
until  the  mercury  flows  over  at  the  top  of  the  tube ;  then  the 
little  cup  is  removed  and  the  tube  hermetically  sealed. 

Graduation. — To  graduate  the  instrument,  it  is  plunged  succes- 
sively into  ice-cold  water,  and  into  steam  escaping  from  boiling 
water ;  the  levels  of  the  mercury  at  these  temperatures  are  then 
marked  32°  and  212°  respectively.  The  space  between  these 
points  is  afterwards  divided  into  180  equal  parts,  and  numbered 
accordingly. 

13.  You  place  one  hand  in  mercury,  and  the  oililr  in  ivater,  both 
liquids  having  the  same  temperature;  the  hand  in  the  mercury  feels 
colder  than  the  hand  in  the  ivater — why  ? 

The  human  body  is  in  general  at  a  higher  temperature  than 
surrounding  objects,  and  as  the  tendency  of  heat  is  to  pass  from 
the  hotter  ""body  to  the  colder,  that  body  feels  the  coldest  which 
conducts  heat  the  most  readily.  Now  mercury  conducts  heat 
much  better  than  water  ;  there  is  therefore  more  heat  abstracted 
from  the  hand  by  the  mercury  than  by  the  water  in  a  given 
time  ;  hence  the  difference  of  sensation.  Were  both  fluids  hotter 
than  the  hand,  the  reverse  sensation  would  be  the  case. 


140  QUESTIONS. 

14.  Describe  the  heating  powers  of  the  various  colours  of  the  solar 
spectrum. 

The  solar  spectrum  is  made  up  of  seven  different  colours,  viz., 
red,  orange,  yellow,  green,  blue,  indigo,  and  violet.  Commencing 
from  the  violet  end,  there  is  very  little  heat  perceptible  ;  the 
heating  power,  however,  gradually  increases  towards  the  red,  a 
little  beyond  which  is  found  the  maximum  heating  power.  The 
heating  powers  of  the  different  colours  are  usually  shown  by  a 
curve  above  the  spectrum,  which  gradually  rises,  until  it  attains 
its  greatest  height  towards  the  red,  a  little  beyond  the  visible 
spectrum,  thereafter  gradually  falling,  till  it  eventually  disappears. 


WILLIAM  COLLINS,    AND   CO.,   PRINTERS,    GLASGOW. 


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